diff --git a/build/types/core b/build/types/core
index 4b16b4812d..b9669ef6ab 100644
--- a/build/types/core
+++ b/build/types/core
@@ -35,8 +35,10 @@
 +../../lib/util/event_manager.js
 +../../lib/util/fake_event.js
 +../../lib/util/fake_event_target.js
++../../lib/util/functional.js
 +../../lib/util/i_destroyable.js
 +../../lib/util/language_utils.js
++../../lib/util/map_utils.js
 +../../lib/util/multi_map.js
 +../../lib/util/pssh.js
 +../../lib/util/public_promise.js
diff --git a/lib/dash/content_protection.js b/lib/dash/content_protection.js
index 10df0119a2..b7f047e976 100644
--- a/lib/dash/content_protection.js
+++ b/lib/dash/content_protection.js
@@ -19,6 +19,8 @@ goog.provide('shaka.dash.ContentProtection');
 
 goog.require('goog.asserts');
 goog.require('shaka.util.Error');
+goog.require('shaka.util.Functional');
+goog.require('shaka.util.MapUtils');
 goog.require('shaka.util.XmlUtils');
 
 
@@ -107,6 +109,8 @@ shaka.dash.ContentProtection.MP4Protection_ =
 shaka.dash.ContentProtection.parseFromAdaptationSet = function(
     elems, callback) {
   var ContentProtection = shaka.dash.ContentProtection;
+  var Functional = shaka.util.Functional;
+  var MapUtils = shaka.util.MapUtils;
   var parsed = ContentProtection.parseElements_(elems);
 
   // Find the default key ID and init data.  Create a new array of all the
@@ -126,12 +130,12 @@ shaka.dash.ContentProtection.parseFromAdaptationSet = function(
 
   // Get the default key ID; if there are multiple, they must all match.
   var keyIds = parsed.map(function(elem) { return elem.keyId; })
-    .filter(function(keyId) { return keyId != null; });
+    .filter(Functional.isNotNull);
   /** @type {?string} */
   var defaultKeyId = null;
   if (keyIds.length > 0) {
     defaultKeyId = keyIds[0];
-    if (keyIds.some(function(keyId) { return keyId != defaultKeyId; })) {
+    if (keyIds.some(Functional.isNotEqualFunc(defaultKeyId))) {
       throw new shaka.util.Error(
           shaka.util.Error.Category.MANIFEST,
           shaka.util.Error.Code.DASH_CONFLICTING_KEY_IDS);
@@ -154,8 +158,7 @@ shaka.dash.ContentProtection.parseFromAdaptationSet = function(
     // supported.
     var keySystems = ContentProtection.defaultKeySystems_;
     drmInfos =
-        Object.keys(keySystems)
-            .map(function(uri) { return keySystems[uri]; })
+        MapUtils.values(keySystems)
             .map(function(keySystem) {
               return ContentProtection.createDrmInfo_(keySystem, defaultInit);
             });
@@ -251,6 +254,7 @@ shaka.dash.ContentProtection.createDrmInfo_ = function(keySystem, initData) {
  */
 shaka.dash.ContentProtection.convertElements_ = function(
     defaultInit, callback, elements) {
+  var Functional = shaka.util.Functional;
   return elements.map(
       /**
        * @param {shaka.dash.ContentProtection.Element} element
@@ -269,7 +273,7 @@ shaka.dash.ContentProtection.convertElements_ = function(
               callback, 'ContentProtection callback is required');
           return callback(element.node) || [];
         }
-      }).reduce(function(all, part) { return all.concat(part); }, []);
+      }).reduce(Functional.collapseArrays, []);
 };
 
 
@@ -282,6 +286,7 @@ shaka.dash.ContentProtection.convertElements_ = function(
  * @private
  */
 shaka.dash.ContentProtection.parseElements_ = function(elems) {
+  var Functional = shaka.util.Functional;
   return elems.map(
       /**
        * @param {!Element} elem
@@ -338,6 +343,6 @@ shaka.dash.ContentProtection.parseElements_ = function(elems) {
           init: (init.length > 0 ? init : null)
         };
         return element;
-      }).filter(function(e) { return e != null; });
+      }).filter(Functional.isNotNull);
 };
 
diff --git a/lib/dash/dash_parser.js b/lib/dash/dash_parser.js
index 738c467409..75a4c696ca 100644
--- a/lib/dash/dash_parser.js
+++ b/lib/dash/dash_parser.js
@@ -29,6 +29,7 @@ goog.require('shaka.media.PresentationTimeline');
 goog.require('shaka.media.SegmentReference');
 goog.require('shaka.net.NetworkingEngine');
 goog.require('shaka.util.Error');
+goog.require('shaka.util.Functional');
 goog.require('shaka.util.LanguageUtils');
 goog.require('shaka.util.MultiMap');
 goog.require('shaka.util.StringUtils');
@@ -361,8 +362,9 @@ shaka.dash.DashParser.prototype.requestManifest_ = function() {
  */
 shaka.dash.DashParser.prototype.parseManifest_ =
     function(data, finalManifestUri) {
-  var XmlUtils = shaka.util.XmlUtils;
   var Error = shaka.util.Error;
+  var Functional = shaka.util.Functional;
+  var XmlUtils = shaka.util.XmlUtils;
 
   var string = shaka.util.StringUtils.fromBytesAutoDetect(data);
   var parser = new DOMParser();
@@ -391,7 +393,7 @@ shaka.dash.DashParser.prototype.parseManifest_ =
   /** @type {!Array.<string>} */
   var locations = XmlUtils.findChildren(mpd, 'Location')
                       .map(XmlUtils.getContents)
-                      .filter(function(l) { return l != null; });
+                      .filter(Functional.isNotNull);
   if (locations.length > 0) {
     this.manifestUris_ = locations;
     manifestBaseUris = locations;
@@ -491,6 +493,7 @@ shaka.dash.DashParser.prototype.parseManifest_ =
  */
 shaka.dash.DashParser.prototype.parsePeriods_ = function(
     context, baseUris, mpd) {
+  var Functional = shaka.util.Functional;
   var XmlUtils = shaka.util.XmlUtils;
   var presentationDuration = XmlUtils.parseAttr(
       mpd, 'mediaPresentationDuration', XmlUtils.parseDuration);
@@ -531,7 +534,7 @@ shaka.dash.DashParser.prototype.parsePeriods_ = function(
     // If there are any new periods, call the callback and add them to the
     // manifest.  If this is the first parse, it will see all of them as new.
     var periodId = context.period.id;
-    if (this.periodIds_.every(function(id) { return id != periodId; })) {
+    if (this.periodIds_.every(Functional.isNotEqualFunc(periodId))) {
       this.filterPeriod_(period);
       this.periodIds_.push(periodId);
       if (this.manifest_)
@@ -887,6 +890,7 @@ shaka.dash.DashParser.prototype.createFrame_ = function(
  * @private
  */
 shaka.dash.DashParser.prototype.createStreamSets_ = function(adaptationSets) {
+  var Functional = shaka.util.Functional;
   /**
    * A map of ID to the group it belongs to.  Multiple IDs can map to the same
    * group.  Each entry in the group will map back to the same array.
@@ -920,9 +924,7 @@ shaka.dash.DashParser.prototype.createStreamSets_ = function(adaptationSets) {
   /** @type {!Array.<!Array.<shaka.dash.DashParser.AdaptationInfo>>} */
   var seenGroups = [];
 
-  // TODO: Use MapUtils.
-  Object.keys(groupMap).map(function(groupId) {
-    var group = groupMap[groupId];
+  shaka.util.MapUtils.values(groupMap).forEach(function(group) {
     if (seenGroups.indexOf(group) >= 0)
       return;
 
@@ -954,10 +956,10 @@ shaka.dash.DashParser.prototype.createStreamSets_ = function(adaptationSets) {
           primary: sets.some(function(s) { return s.main; }),
           drmInfos:
               sets.map(function(s) { return s.drmInfos; })
-                  .reduce(function(all, part) { return all.concat(part); }, []),
+                  .reduce(Functional.collapseArrays, []),
           streams:
               sets.map(function(s) { return s.streams; })
-                  .reduce(function(all, part) { return all.concat(part); }, [])
+                  .reduce(Functional.collapseArrays, [])
         };
         ret.push(streamSet);
       });  // forEach lang
@@ -1043,45 +1045,44 @@ shaka.dash.DashParser.prototype.requestForTiming_ = function(uri, method) {
 /**
  * Parses an array of UTCTiming elements.
  *
- * @param {Array.<!Element>} elems
+ * @param {!Array.<!Element>} elems
  * @return {!Promise.<number>}
  * @private
  */
 shaka.dash.DashParser.prototype.parseUtcTiming_ = function(elems) {
-  var promise = elems.reduce(function(parent, elem) {
-    return parent.catch(function() {
-      var scheme = elem.getAttribute('schemeIdUri');
-      var value = elem.getAttribute('value');
-      switch (scheme) {
-        // See DASH IOP Guidelines Section 4.7
-        // http://goo.gl/CQFNJT
-        case 'urn:mpeg:dash:utc:http-head:2014':
-        // Some old ISO23009-1 drafts used 2012.
-        case 'urn:mpeg:dash:utc:http-head:2012':
-          return this.requestForTiming_(value, 'HEAD');
-        case 'urn:mpeg:dash:utc:http-xsdate:2014':
-        case 'urn:mpeg:dash:utc:http-iso:2014':
-        case 'urn:mpeg:dash:utc:http-xsdate:2012':
-        case 'urn:mpeg:dash:utc:http-iso:2012':
-          return this.requestForTiming_(value, 'GET');
-        case 'urn:mpeg:dash:utc:direct:2014':
-        case 'urn:mpeg:dash:utc:direct:2012':
-          var date = Date.parse(value);
-          return isNaN(date) ? 0 : (date - Date.now());
-
-        case 'urn:mpeg:dash:utc:http-ntp:2014':
-        case 'urn:mpeg:dash:utc:ntp:2014':
-        case 'urn:mpeg:dash:utc:sntp:2014':
-          shaka.log.warning('NTP UTCTiming scheme is not supported');
-          return Promise.reject();
-        default:
-          shaka.log.warning('Unrecognized scheme in UTCTiming element', scheme);
-          return Promise.reject();
-      }
-    }.bind(this));
-  }.bind(this), Promise.reject());
-
-  return promise.catch(function() { return 0; });
+  var Functional = shaka.util.Functional;
+  return Functional.createFallbackPromiseChain(elems, function(elem) {
+    var scheme = elem.getAttribute('schemeIdUri');
+    var value = elem.getAttribute('value');
+    switch (scheme) {
+      // See DASH IOP Guidelines Section 4.7
+      // http://goo.gl/CQFNJT
+      case 'urn:mpeg:dash:utc:http-head:2014':
+      // Some old ISO23009-1 drafts used 2012.
+      case 'urn:mpeg:dash:utc:http-head:2012':
+        return this.requestForTiming_(value, 'HEAD');
+      case 'urn:mpeg:dash:utc:http-xsdate:2014':
+      case 'urn:mpeg:dash:utc:http-iso:2014':
+      case 'urn:mpeg:dash:utc:http-xsdate:2012':
+      case 'urn:mpeg:dash:utc:http-iso:2012':
+        return this.requestForTiming_(value, 'GET');
+      case 'urn:mpeg:dash:utc:direct:2014':
+      case 'urn:mpeg:dash:utc:direct:2012':
+        var date = Date.parse(value);
+        return isNaN(date) ? 0 : (date - Date.now());
+
+      case 'urn:mpeg:dash:utc:http-ntp:2014':
+      case 'urn:mpeg:dash:utc:ntp:2014':
+      case 'urn:mpeg:dash:utc:sntp:2014':
+        shaka.log.warning('NTP UTCTiming scheme is not supported');
+        return Promise.reject();
+      default:
+        shaka.log.warning(
+            'Unrecognized scheme in UTCTiming element', scheme);
+        return Promise.reject();
+    }
+  }.bind(this))
+  .catch(function() { return 0; });
 };
 
 
diff --git a/lib/dash/mpd_utils.js b/lib/dash/mpd_utils.js
index c3b47f2858..ea9bd4b2b3 100644
--- a/lib/dash/mpd_utils.js
+++ b/lib/dash/mpd_utils.js
@@ -21,6 +21,7 @@ goog.require('goog.Uri');
 goog.require('goog.asserts');
 goog.require('shaka.log');
 goog.require('shaka.media.SegmentReference');
+goog.require('shaka.util.Functional');
 goog.require('shaka.util.XmlUtils');
 
 
@@ -352,6 +353,7 @@ shaka.dash.MpdUtils.fitSegmentReferences = function(
  * @return {!Array.<string>}
  */
 shaka.dash.MpdUtils.resolveUris = function(baseUris, relativeUris) {
+  var Functional = shaka.util.Functional;
   if (relativeUris.length == 0)
     return baseUris;
 
@@ -361,7 +363,7 @@ shaka.dash.MpdUtils.resolveUris = function(baseUris, relativeUris) {
   // Then flatten the Arrays into a single Array.
   return baseUris.map(function(uri) { return new goog.Uri(uri); })
     .map(function(base) { return relativeAsGoog.map(base.resolve.bind(base)); })
-    .reduce(function(all, part) { return all.concat(part); }, [])
+    .reduce(Functional.collapseArrays, [])
     .map(function(uri) { return uri.toString(); });
 };
 
@@ -432,6 +434,7 @@ shaka.dash.MpdUtils.parseSegmentInfo = function(context, callback) {
  * @return {?string}
  */
 shaka.dash.MpdUtils.inheritAttribute = function(context, callback, attribute) {
+  var Functional = shaka.util.Functional;
   goog.asserts.assert(
       callback(context.representation),
       'There must be at least one element of the given type');
@@ -441,7 +444,7 @@ shaka.dash.MpdUtils.inheritAttribute = function(context, callback, attribute) {
     callback(context.representation),
     callback(context.adaptationSet),
     callback(context.period)
-  ].filter(function(s) { return s != null; });
+  ].filter(Functional.isNotNull);
 
   return nodes
       .map(function(s) { return s.getAttribute(attribute); })
@@ -459,6 +462,7 @@ shaka.dash.MpdUtils.inheritAttribute = function(context, callback, attribute) {
  * @return {Element}
  */
 shaka.dash.MpdUtils.inheritChild = function(context, callback, child) {
+  var Functional = shaka.util.Functional;
   goog.asserts.assert(
       callback(context.representation),
       'There must be at least one element of the given type');
@@ -468,7 +472,7 @@ shaka.dash.MpdUtils.inheritChild = function(context, callback, child) {
     callback(context.representation),
     callback(context.adaptationSet),
     callback(context.period)
-  ].filter(function(s) { return s != null; });
+  ].filter(Functional.isNotNull);
 
   var XmlUtils = shaka.util.XmlUtils;
   return nodes
diff --git a/lib/dash/segment_list.js b/lib/dash/segment_list.js
index 832e492c26..88a6b7e13f 100644
--- a/lib/dash/segment_list.js
+++ b/lib/dash/segment_list.js
@@ -23,6 +23,7 @@ goog.require('shaka.dash.SegmentBase');
 goog.require('shaka.media.SegmentIndex');
 goog.require('shaka.media.SegmentReference');
 goog.require('shaka.util.Error');
+goog.require('shaka.util.Functional');
 goog.require('shaka.util.XmlUtils');
 
 
@@ -295,12 +296,13 @@ shaka.dash.SegmentList.createSegmentReferences_ = function(
  * @private
  */
 shaka.dash.SegmentList.parseMediaSegments_ = function(context) {
+  var Functional = shaka.util.Functional;
   /** @type {!Array.<!Element>} */
   var segmentLists = [
     context.representation.segmentList,
     context.adaptationSet.segmentList,
     context.period.segmentList
-  ].filter(function(s) { return s != null; });
+  ].filter(Functional.isNotNull);
 
   var XmlUtils = shaka.util.XmlUtils;
   // Search each SegmentList for one with at least one SegmentURL element,
diff --git a/lib/media/drm_engine.js b/lib/media/drm_engine.js
index 8c9b56e717..05de9fcd1d 100644
--- a/lib/media/drm_engine.js
+++ b/lib/media/drm_engine.js
@@ -22,6 +22,7 @@ goog.require('shaka.log');
 goog.require('shaka.util.ArrayUtils');
 goog.require('shaka.util.Error');
 goog.require('shaka.util.EventManager');
+goog.require('shaka.util.Functional');
 goog.require('shaka.util.IDestroyable');
 goog.require('shaka.util.PublicPromise');
 goog.require('shaka.util.Uint8ArrayUtils');
@@ -92,13 +93,14 @@ shaka.media.DrmEngine.ActiveSession;
 
 /** @override */
 shaka.media.DrmEngine.prototype.destroy = function() {
+  var Functional = shaka.util.Functional;
   this.destroyed_ = true;
 
   this.activeSessions_.forEach(function(activeSession) {
     // Ignore any errors when closing the sessions.  One such error would be
     // an invalid state error triggered by closing a session which has not
     // generated any key requests.
-    activeSession.session.close().catch(function() {});
+    activeSession.session.close().catch(Functional.noop);
   });
 
   var async = [];
@@ -107,7 +109,7 @@ shaka.media.DrmEngine.prototype.destroy = function() {
 
   if (this.video_) {
     goog.asserts.assert(!this.video_.src, 'video src must be removed first!');
-    async.push(this.video_.setMediaKeys(null).catch(function() {}));
+    async.push(this.video_.setMediaKeys(null).catch(Functional.noop));
   }
 
   this.drmInfos_ = [];
@@ -428,6 +430,7 @@ shaka.media.DrmEngine.prototype.queryMediaKeys_ =
  * @private
  */
 shaka.media.DrmEngine.prototype.fillInDrmInfoDefaults_ = function(drmInfo) {
+  var MapUtils = shaka.util.MapUtils;
   var keySystem = drmInfo.keySystem;
 
   if (!keySystem) {
@@ -441,7 +444,7 @@ shaka.media.DrmEngine.prototype.fillInDrmInfoDefaults_ = function(drmInfo) {
     if (server) {
       drmInfo.licenseServerUri = server;
     } else if (keySystem == 'org.w3.clearkey') {
-      var hasClearKeys = Object.keys(this.config_.clearKeys).length != 0;
+      var hasClearKeys = !MapUtils.empty(this.config_.clearKeys);
       if (hasClearKeys) {
         this.configureClearKey_(drmInfo);
       } else {
diff --git a/lib/media/media_source_engine.js b/lib/media/media_source_engine.js
index 4c46194aa3..544899235b 100644
--- a/lib/media/media_source_engine.js
+++ b/lib/media/media_source_engine.js
@@ -22,6 +22,7 @@ goog.require('shaka.media.TextEngine');
 goog.require('shaka.media.TimeRangesUtils');
 goog.require('shaka.util.Error');
 goog.require('shaka.util.EventManager');
+goog.require('shaka.util.Functional');
 goog.require('shaka.util.IDestroyable');
 goog.require('shaka.util.PublicPromise');
 
@@ -162,6 +163,7 @@ shaka.media.MediaSourceEngine.support = function() {
  * @override
  */
 shaka.media.MediaSourceEngine.prototype.destroy = function() {
+  var Functional = shaka.util.Functional;
   this.destroyed_ = true;
 
   var cleanup = [];
@@ -176,12 +178,12 @@ shaka.media.MediaSourceEngine.prototype.destroy = function() {
 
     // We will wait for this item to complete/fail.
     if (inProgress) {
-      cleanup.push(inProgress.p.catch(function() {}));
+      cleanup.push(inProgress.p.catch(Functional.noop));
     }
 
     // The rest will be rejected silently if possible.
     for (var i = 1; i < q.length; ++i) {
-      q[i].p.catch(function() {});
+      q[i].p.catch(Functional.noop);
       q[i].p.reject();
     }
   }
diff --git a/lib/media/streaming_engine.js b/lib/media/streaming_engine.js
index e55fcba0b6..d0fa439569 100644
--- a/lib/media/streaming_engine.js
+++ b/lib/media/streaming_engine.js
@@ -22,7 +22,9 @@ goog.require('shaka.media.MediaSourceEngine');
 goog.require('shaka.media.Playhead');
 goog.require('shaka.net.NetworkingEngine');
 goog.require('shaka.util.Error');
+goog.require('shaka.util.Functional');
 goog.require('shaka.util.IDestroyable');
+goog.require('shaka.util.MapUtils');
 goog.require('shaka.util.PublicPromise');
 
 
@@ -311,6 +313,7 @@ shaka.media.StreamingEngine.prototype.configure = function(config) {
  * @return {!Promise}
  */
 shaka.media.StreamingEngine.prototype.init = function() {
+  var MapUtils = shaka.util.MapUtils;
   goog.asserts.assert(this.config_,
       'StreamingEngine configure() must be called before init()!');
 
@@ -321,7 +324,7 @@ shaka.media.StreamingEngine.prototype.init = function() {
   // Get the initial set of Streams.
   var streamsByType =
       this.onChooseStreams_(this.manifest_.periods[needPeriodIndex]);
-  if (Object.keys(streamsByType).length == 0) {
+  if (MapUtils.empty(streamsByType)) {
     shaka.log.error('init: no Streams chosen');
     return Promise.reject(new shaka.util.Error(
         shaka.util.Error.Category.STREAMING,
@@ -361,11 +364,9 @@ shaka.media.StreamingEngine.prototype.getCurrentPeriod = function() {
  */
 shaka.media.StreamingEngine.prototype.getActiveStreams = function() {
   goog.asserts.assert(this.mediaStates_, 'Must be initialized');
-  var activeStreams = {};
-  Object.keys(this.mediaStates_).map(function(type) {
-    activeStreams[type] = this.mediaStates_[type].stream;
-  }.bind(this));
-  return activeStreams;
+  var MapUtils = shaka.util.MapUtils;
+  return MapUtils.map(
+      this.mediaStates_, function(state) { return state.stream; });
 };
 
 
@@ -525,6 +526,7 @@ shaka.media.StreamingEngine.prototype.seeked = function() {
  * @private
  */
 shaka.media.StreamingEngine.prototype.initStreams_ = function(streamsByType) {
+  var MapUtils = shaka.util.MapUtils;
   goog.asserts.assert(this.config_,
       'StreamingEngine configure() must be called before init()!');
 
@@ -533,23 +535,17 @@ shaka.media.StreamingEngine.prototype.initStreams_ = function(streamsByType) {
   var needPeriodIndex = this.findPeriodContainingTime_(playheadTime);
 
   // Init MediaSourceEngine.
-  var typeConfig = {};
-
-  for (var type in streamsByType) {
-    var stream = streamsByType[type];
-    typeConfig[type] =
-        stream.mimeType +
+  var typeConfig = MapUtils.map(streamsByType, function(stream) {
+    return stream.mimeType +
         (stream.codecs ? '; codecs="' + stream.codecs + '"' : '');
-  }
+  });
 
   this.mediaSourceEngine_.init(typeConfig);
   this.setDuration_();
 
   // Setup the initial set of Streams and then begin each update cycle. After
   // startup completes onUpdate_() will set up the remaining Periods.
-  // TODO: Use MapUtils.
-  var streams = Object.keys(streamsByType)
-      .map(function(type) { return streamsByType[type]; });
+  var streams = MapUtils.values(streamsByType);
   return this.setupStreams_(streams).then(function() {
     for (var type in streamsByType) {
       var stream = streamsByType[type];
@@ -586,6 +582,7 @@ shaka.media.StreamingEngine.prototype.initStreams_ = function(streamsByType) {
  * @private
  */
 shaka.media.StreamingEngine.prototype.setupPeriod_ = function(periodIndex) {
+  var Functional = shaka.util.Functional;
   var canSwitchRecord = this.canSwitchPeriod_[periodIndex];
   if (canSwitchRecord) {
     shaka.log.debug(
@@ -603,7 +600,7 @@ shaka.media.StreamingEngine.prototype.setupPeriod_ = function(periodIndex) {
 
   var streams = this.manifest_.periods[periodIndex].streamSets
       .map(function(streamSet) { return streamSet.streams; })
-      .reduce(function(all, part) { return all.concat(part); }, []);
+      .reduce(Functional.collapseArrays, []);
 
   // Serialize Period set up.
   this.setupPeriodPromise_ = this.setupPeriodPromise_.then(function() {
@@ -700,6 +697,7 @@ shaka.media.StreamingEngine.prototype.setDuration_ = function() {
  * @private
  */
 shaka.media.StreamingEngine.prototype.onUpdate_ = function(mediaState) {
+  var MapUtils = shaka.util.MapUtils;
   if (this.destroyed_) return;
 
   var logPrefix = shaka.media.StreamingEngine.logPrefix_(mediaState);
@@ -736,10 +734,8 @@ shaka.media.StreamingEngine.prototype.onUpdate_ = function(mediaState) {
     return;
   }
 
-  // TODO: Use MapUtils.
   goog.asserts.assert(this.mediaStates_, 'must not be destroyed');
-  var mediaStates = Object.keys(this.mediaStates_)
-      .map(function(type) { return this.mediaStates_[type]; }.bind(this));
+  var mediaStates = MapUtils.values(this.mediaStates_);
 
   // Handle startup and re- buffering.
   this.playhead_.setBuffering(
@@ -1240,16 +1236,18 @@ shaka.media.StreamingEngine.prototype.append_ = function(
  */
 shaka.media.StreamingEngine.prototype.evict_ = function(
     mediaState, playheadTime) {
+  var MapUtils = shaka.util.MapUtils;
   var logPrefix = shaka.media.StreamingEngine.logPrefix_(mediaState);
   shaka.log.v2(logPrefix, 'checking buffer length');
 
   // Get the earliest start time.
-  var startTime = Number.POSITIVE_INFINITY;
-  for (var type in this.mediaStates_) {
-    var ms = this.mediaStates_[type];
-    startTime = Math.min(this.mediaSourceEngine_.bufferStart(ms.type),
-                         startTime);
-  }
+  goog.asserts.assert(this.mediaStates_, 'Must be initialized');
+  var mediaStates = MapUtils.values(this.mediaStates_);
+  var times = mediaStates.map(function(state) {
+    return this.mediaSourceEngine_.bufferStart(state.type);
+  }.bind(this));
+  var startTime = Math.min.apply(Math, times);
+
   goog.asserts.assert(startTime != Number.POSITIVE_INFINITY,
                       'startTime should not be infinity');
   var bufferedBehind = playheadTime - startTime;
@@ -1272,12 +1270,10 @@ shaka.media.StreamingEngine.prototype.evict_ = function(
                'bufferBehind=' + this.config_.bufferBehind,
                'overflow=' + overflow);
 
-  var async = [];
-  for (var type in this.mediaStates_) {
-    var ms = this.mediaStates_[type];
-    async.push(this.mediaSourceEngine_.remove(
-        ms.type, startTime, startTime + overflow));
-  }
+  var async = mediaStates.map(function(state) {
+    return this.mediaSourceEngine_.remove(
+        state.type, startTime, startTime + overflow);
+  }.bind(this));
 
   return Promise.all(async).then(function() {
     if (this.destroyed_) return;
@@ -1342,15 +1338,15 @@ shaka.media.StreamingEngine.prototype.handleDrift_ = function(
  * @private
  */
 shaka.media.StreamingEngine.prototype.handleStartup_ = function(mediaState) {
+  var Functional = shaka.util.Functional;
+  var MapUtils = shaka.util.MapUtils;
   if (this.startupComplete_)
     return;
 
   var logPrefix = shaka.media.StreamingEngine.logPrefix_(mediaState);
 
-  // TODO: Use MapUtils.
   goog.asserts.assert(this.mediaStates_, 'must not be destroyed');
-  var mediaStates = Object.keys(this.mediaStates_)
-      .map(function(type) { return this.mediaStates_[type]; }.bind(this));
+  var mediaStates = MapUtils.values(this.mediaStates_);
   this.startupComplete_ = mediaStates.every(function(ms) {
     // Startup completes once we have buffered at least one segment from each
     // MediaState, have handled positive or large negative drift, and are not
@@ -1386,12 +1382,12 @@ shaka.media.StreamingEngine.prototype.handleStartup_ = function(mediaState) {
     this.setupPeriod_(currentPeriodIndex).then(function() {
       shaka.log.v1(logPrefix, 'calling onCanSwitch_()...');
       this.onCanSwitch_();
-    }.bind(this)).catch(function() {});
+    }.bind(this)).catch(Functional.noop);
   }
 
   // Now setup all known Periods.
   for (var i = 0; i < this.manifest_.periods.length; ++i) {
-    this.setupPeriod_(i).catch(function() {});
+    this.setupPeriod_(i).catch(Functional.noop);
   }
 
   if (this.onStartupComplete_) {
@@ -1410,6 +1406,8 @@ shaka.media.StreamingEngine.prototype.handleStartup_ = function(mediaState) {
  */
 shaka.media.StreamingEngine.prototype.handlePeriodTransition_ = function(
     mediaState) {
+  var Functional = shaka.util.Functional;
+  var MapUtils = shaka.util.MapUtils;
   var logPrefix = shaka.media.StreamingEngine.logPrefix_(mediaState);
 
   var currentPeriodIndex = this.findPeriodContainingStream_(mediaState.stream);
@@ -1418,10 +1416,8 @@ shaka.media.StreamingEngine.prototype.handlePeriodTransition_ = function(
 
   var needPeriodIndex = mediaState.needPeriodIndex;
 
-  // TODO: Use MapUtils.
   goog.asserts.assert(this.mediaStates_, 'must not be destroyed');
-  var mediaStates = Object.keys(this.mediaStates_)
-      .map(function(type) { return this.mediaStates_[type]; }.bind(this));
+  var mediaStates = MapUtils.values(this.mediaStates_);
 
   // Only call onChooseStreams_() when all MediaStates need the same Period.
   var needSamePeriod = mediaStates.every(function(ms) {
@@ -1434,9 +1430,7 @@ shaka.media.StreamingEngine.prototype.handlePeriodTransition_ = function(
   }
 
   // Only call onChooseStreams_() once per Period transition.
-  var allAreIdle = mediaStates.every(function(ms) {
-    return shaka.media.StreamingEngine.isIdle_(ms);
-  });
+  var allAreIdle = mediaStates.every(shaka.media.StreamingEngine.isIdle_);
   if (!allAreIdle) {
     shaka.log.debug(
         logPrefix,
@@ -1497,7 +1491,7 @@ shaka.media.StreamingEngine.prototype.handlePeriodTransition_ = function(
     // We've already set up the Period so call onCanSwitch_() right now.
     shaka.log.v1(logPrefix, 'calling onCanSwitch_()...');
     this.onCanSwitch_();
-  }.bind(this)).catch(function() {});
+  }.bind(this)).catch(Functional.noop);
 };
 
 
diff --git a/lib/net/networking_engine.js b/lib/net/networking_engine.js
index f3a8d4220f..62dacb7e16 100644
--- a/lib/net/networking_engine.js
+++ b/lib/net/networking_engine.js
@@ -20,6 +20,7 @@ goog.provide('shaka.net.NetworkingEngine');
 goog.require('goog.Uri');
 goog.require('goog.asserts');
 goog.require('shaka.util.Error');
+goog.require('shaka.util.Functional');
 goog.require('shaka.util.IDestroyable');
 goog.require('shaka.util.PublicPromise');
 
@@ -230,13 +231,14 @@ shaka.net.NetworkingEngine.makeRequest = function(
 
 /** @override */
 shaka.net.NetworkingEngine.prototype.destroy = function() {
+  var Functional = shaka.util.Functional;
   this.destroyed_ = true;
   this.requestFilters_ = [];
   this.responseFilters_ = [];
 
   var cleanup = [];
   for (var i = 0; i < this.requests_.length; ++i) {
-    cleanup.push(this.requests_[i].catch(function() {}));
+    cleanup.push(this.requests_[i].catch(Functional.noop));
   }
   return Promise.all(cleanup);
 };
diff --git a/lib/player.js b/lib/player.js
index 8fbb03c9ca..acbcd12756 100644
--- a/lib/player.js
+++ b/lib/player.js
@@ -32,6 +32,7 @@ goog.require('shaka.util.Error');
 goog.require('shaka.util.EventManager');
 goog.require('shaka.util.FakeEvent');
 goog.require('shaka.util.FakeEventTarget');
+goog.require('shaka.util.Functional');
 goog.require('shaka.util.IDestroyable');
 goog.require('shaka.util.LanguageUtils');
 goog.require('shaka.util.PublicPromise');
@@ -562,6 +563,7 @@ shaka.Player.prototype.cancelTrickPlay = function() {
  * @export
  */
 shaka.Player.prototype.getTracks = function() {
+  var Functional = shaka.util.Functional;
   if (!this.streamingEngine_)
     return [];
 
@@ -584,7 +586,7 @@ shaka.Player.prototype.getTracks = function() {
           };
         });
       })
-      .reduce(function(all, part) { return all.concat(part); }, []);
+      .reduce(Functional.collapseArrays, []);
 };
 
 
diff --git a/lib/util/functional.js b/lib/util/functional.js
new file mode 100644
index 0000000000..038dd7ff99
--- /dev/null
+++ b/lib/util/functional.js
@@ -0,0 +1,102 @@
+/**
+ * @license
+ * Copyright 2016 Google Inc.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+goog.provide('shaka.util.Functional');
+
+
+/**
+ * @namespace shaka.util.Functional
+ * @summary A set of functional utility functions.
+ */
+
+
+/**
+ * Creates a promise chain that calls the given callback for each element in
+ * the array in a catch of a promise.
+ *
+ * e.g.:
+ * Promise.reject().catch(callback(array[0])).catch(callback(array[1]));
+ *
+ * @param {!Array.<ELEM>} array
+ * @param {function(ELEM):!Promise.<RESULT>} callback
+ * @return {!Promise.<RESULT>}
+ * @template ELEM,RESULT
+ */
+shaka.util.Functional.createFallbackPromiseChain = function(array, callback) {
+  return array.reduce(function(callback, promise, elem) {
+    return promise.catch(callback.bind(null, elem));
+  }.bind(null, callback), Promise.reject());
+};
+
+
+/**
+ * Returns the first array concatenated to the second; used to collapse an
+ * array of arrays into a single array.
+ *
+ * @param {!Array.<T>} all
+ * @param {!Array.<T>} part
+ * @return {!Array.<T>}
+ * @template T
+ */
+shaka.util.Functional.collapseArrays = function(all, part) {
+  return all.concat(part);
+};
+
+
+/**
+ * A no-op function.  Useful in promise chains.
+ */
+shaka.util.Functional.noop = function() {};
+
+
+/**
+ * Returns if the given value is not null; useful for filtering out null values.
+ *
+ * @param {T} value
+ * @return {boolean}
+ * @template T
+ */
+shaka.util.Functional.isNotNull = function(value) {
+  return value != null;
+};
+
+
+/**
+ * Creates a function that returns whether the given value is equal to the given
+ * value.
+ *
+ * @param {T} compare
+ * @return {function(T):boolean}
+ * @template T
+ */
+shaka.util.Functional.isEqualFunc = function(compare) {
+  return function(a) { return a == compare; };
+};
+
+
+/**
+ * Creates a function that returns whether the given value is not equal to the
+ * given value.
+ *
+ * @param {T} compare
+ * @return {function(T):boolean}
+ * @template T
+ */
+shaka.util.Functional.isNotEqualFunc = function(compare) {
+  return function(a) { return a != compare; };
+};
+
diff --git a/lib/util/map_utils.js b/lib/util/map_utils.js
new file mode 100644
index 0000000000..553d0f4983
--- /dev/null
+++ b/lib/util/map_utils.js
@@ -0,0 +1,65 @@
+/**
+ * @license
+ * Copyright 2016 Google Inc.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+goog.provide('shaka.util.MapUtils');
+
+
+/**
+ * @namespace shaka.util.MapUtils
+ * @summary A set of map/object utility functions.
+ */
+
+
+/**
+ * Returns true if the map is empty; otherwise, returns false.
+ *
+ * @param {Object.<KEY, VALUE>} object
+ * @return {boolean}
+ * @template KEY,VALUE
+ */
+shaka.util.MapUtils.empty = function(object) {
+  return !object || Object.keys(object).length == 0;
+};
+
+
+/**
+ * Gets the map's values.
+ *
+ * @param {!Object.<KEY, VALUE>} object
+ * @return {!Array.<VALUE>}
+ * @template KEY,VALUE
+ */
+shaka.util.MapUtils.values = function(object) {
+  return Object.keys(object).map(function(key) { return object[key]; });
+};
+
+
+/**
+ * Converts the values in the given Map to a different value.
+ *
+ * @param {!Object.<KEY, VALUE>} object
+ * @param {function(VALUE, KEY=):OUTPUT} callback
+ * @return {!Object.<KEY, OUTPUT>}
+ * @template KEY,VALUE,OUTPUT
+ */
+shaka.util.MapUtils.map = function(object, callback) {
+  return Object.keys(object).reduce(function(ret, key) {
+    var value = object[key];
+    ret[key] = callback(value, key);
+    return ret;
+  }, {});
+};
diff --git a/lib/util/xml_utils.js b/lib/util/xml_utils.js
index 8ee39d8bdf..abe04df039 100644
--- a/lib/util/xml_utils.js
+++ b/lib/util/xml_utils.js
@@ -30,19 +30,10 @@ goog.require('shaka.log');
  *   child XML element with the given tag name.
  */
 shaka.util.XmlUtils.findChild = function(elem, name) {
-  var childElement = null;
-
-  for (var i = 0; i < elem.childNodes.length; i++) {
-    if (elem.childNodes[i].tagName != name)
-      continue;
-    if (childElement)
-      return null;
-    childElement = elem.childNodes[i];
-  }
-
-  goog.asserts.assert(!childElement || childElement instanceof Element,
-                      'child element should be an Element');
-  return childElement;
+  var children = shaka.util.XmlUtils.findChildren(elem, name);
+  if (children.length != 1)
+    return null;
+  return children[0];
 };
 
 
@@ -53,14 +44,12 @@ shaka.util.XmlUtils.findChild = function(elem, name) {
  * @return {!Array.<!Element>} The child XML elements.
  */
 shaka.util.XmlUtils.findChildren = function(elem, name) {
-  var childElements = [];
-
-  for (var i = 0; i < elem.childNodes.length; i++) {
-    if (elem.childNodes[i].tagName == name)
-      childElements.push(elem.childNodes[i]);
-  }
-
-  return childElements;
+  return Array.prototype.filter.call(elem.childNodes, function(child) {
+    goog.asserts.assert(
+        child.tagName != name || child instanceof Element,
+        'child element should be an Element');
+    return child.tagName == name;
+  });
 };