diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index 46464a3ecf420..cef34a3af0136 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -780,6 +780,7 @@ Performance improvements
 - Performance improvement in :func:`merge` when not merging on the index - the new index will now be :class:`RangeIndex` instead of :class:`Int64Index` (:issue:`49478`)
 - Performance improvement in :meth:`DataFrame.to_dict` and :meth:`Series.to_dict` when using any non-object dtypes (:issue:`46470`)
 - Performance improvement in :func:`read_html` when there are multiple tables (:issue:`49929`)
+- Performance improvement in :func:`to_datetime` when using ``'%Y%m%d'`` format (:issue:`17410`)
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_200.bug_fixes:
@@ -809,6 +810,13 @@ Datetimelike
 - Bug in :meth:`Timestamp.round` when the ``freq`` argument has zero-duration (e.g. "0ns") returning incorrect results instead of raising (:issue:`49737`)
 - Bug in :func:`to_datetime` was not raising ``ValueError`` when invalid format was passed and ``errors`` was ``'ignore'`` or ``'coerce'`` (:issue:`50266`)
 - Bug in :class:`DateOffset` was throwing ``TypeError`` when constructing with milliseconds and another super-daily argument (:issue:`49897`)
+- Bug in :func:`to_datetime` was not raising ``ValueError`` when parsing string with decimal date with format ``'%Y%m%d'`` (:issue:`50051`)
+- Bug in :func:`to_datetime` was not converting ``None`` to ``NaT`` when parsing mixed-offset date strings with ISO8601 format (:issue:`50071`)
+- Bug in :func:`to_datetime` was not returning input when parsing out-of-bounds date string with ``errors='ignore'`` and ``format='%Y%m%d'`` (:issue:`14487`)
+- Bug in :func:`to_datetime` was converting timezone-naive ``datetime.datetime`` to timezone-aware when parsing with timezone-aware strings, ISO8601 format, and ``utc=False`` (:issue:`50254`)
+- Bug in :func:`to_datetime` was throwing ``ValueError`` when parsing dates with ISO8601 format where some values were not zero-padded (:issue:`21422`)
+- Bug in :func:`to_datetime` was giving incorrect results when using ``format='%Y%m%d'`` and ``errors='ignore'`` (:issue:`26493`)
+- Bug in :func:`to_datetime` was failing to parse date strings ``'today'`` and ``'now'`` if ``format`` was not ISO8601 (:issue:`50359`)
 -
 
 Timedelta
diff --git a/pandas/_libs/tslib.pyi b/pandas/_libs/tslib.pyi
index ab94c4d59c5fc..9819b5173db56 100644
--- a/pandas/_libs/tslib.pyi
+++ b/pandas/_libs/tslib.pyi
@@ -23,9 +23,6 @@ def array_to_datetime(
     dayfirst: bool = ...,
     yearfirst: bool = ...,
     utc: bool = ...,
-    require_iso8601: bool = ...,
-    format: str | None = ...,
-    exact: bool = ...,
 ) -> tuple[np.ndarray, tzinfo | None]: ...
 
 # returned ndarray may be object dtype or datetime64[ns]
diff --git a/pandas/_libs/tslib.pyx b/pandas/_libs/tslib.pyx
index feae7fc4344d9..acee56a6598c2 100644
--- a/pandas/_libs/tslib.pyx
+++ b/pandas/_libs/tslib.pyx
@@ -38,6 +38,7 @@ from pandas._libs.tslibs.np_datetime cimport (
     pydatetime_to_dt64,
     string_to_dts,
 )
+from pandas._libs.tslibs.strptime cimport parse_today_now
 from pandas._libs.util cimport (
     is_datetime64_object,
     is_float_object,
@@ -443,9 +444,6 @@ cpdef array_to_datetime(
     bint dayfirst=False,
     bint yearfirst=False,
     bint utc=False,
-    bint require_iso8601=False,
-    format: str | None=None,
-    bint exact=True,
 ):
     """
     Converts a 1D array of date-like values to a numpy array of either:
@@ -472,8 +470,6 @@ cpdef array_to_datetime(
          yearfirst parsing behavior when encountering datetime strings
     utc : bool, default False
          indicator whether the dates should be UTC
-    require_iso8601 : bool, default False
-         indicator whether the datetime string should be iso8601
 
     Returns
     -------
@@ -544,16 +540,6 @@ cpdef array_to_datetime(
                     iresult[i] = get_datetime64_nanos(val, NPY_FR_ns)
 
                 elif is_integer_object(val) or is_float_object(val):
-                    if require_iso8601:
-                        if is_coerce:
-                            iresult[i] = NPY_NAT
-                            continue
-                        elif is_raise:
-                            raise ValueError(
-                                f"time data \"{val}\" doesn't "
-                                f"match format \"{format}\", at position {i}"
-                            )
-                        return values, tz_out
                     # these must be ns unit by-definition
                     seen_integer = True
 
@@ -584,25 +570,13 @@ cpdef array_to_datetime(
 
                     string_to_dts_failed = string_to_dts(
                         val, &dts, &out_bestunit, &out_local,
-                        &out_tzoffset, False, format, exact
+                        &out_tzoffset, False, None, False
                     )
                     if string_to_dts_failed:
                         # An error at this point is a _parsing_ error
                         # specifically _not_ OutOfBoundsDatetime
-                        if _parse_today_now(val, &iresult[i], utc):
+                        if parse_today_now(val, &iresult[i], utc):
                             continue
-                        elif require_iso8601:
-                            # if requiring iso8601 strings, skip trying
-                            # other formats
-                            if is_coerce:
-                                iresult[i] = NPY_NAT
-                                continue
-                            elif is_raise:
-                                raise ValueError(
-                                    f"time data \"{val}\" doesn't "
-                                    f"match format \"{format}\", at position {i}"
-                                )
-                            return values, tz_out
 
                         try:
                             py_dt = parse_datetime_string(val,
@@ -665,18 +639,6 @@ cpdef array_to_datetime(
                 if is_coerce:
                     iresult[i] = NPY_NAT
                     continue
-                elif require_iso8601 and isinstance(val, str):
-                    # GH#19382 for just-barely-OutOfBounds falling back to
-                    # dateutil parser will return incorrect result because
-                    # it will ignore nanoseconds
-                    if is_raise:
-
-                        # Still raise OutOfBoundsDatetime,
-                        # as error message is informative.
-                        raise
-
-                    assert is_ignore
-                    return values, tz_out
                 raise
 
     except OutOfBoundsDatetime:
@@ -835,26 +797,6 @@ cdef _array_to_datetime_object(
     return oresult, None
 
 
-cdef bint _parse_today_now(str val, int64_t* iresult, bint utc):
-    # We delay this check for as long as possible
-    # because it catches relatively rare cases
-
-    # Multiply by 1000 to convert to nanos, since these methods naturally have
-    #  microsecond resolution
-    if val == "now":
-        if utc:
-            iresult[0] = Timestamp.utcnow().value * 1000
-        else:
-            # GH#18705 make sure to_datetime("now") matches Timestamp("now")
-            # Note using Timestamp.now() is faster than Timestamp("now")
-            iresult[0] = Timestamp.now().value * 1000
-        return True
-    elif val == "today":
-        iresult[0] = Timestamp.today().value * 1000
-        return True
-    return False
-
-
 def array_to_datetime_with_tz(ndarray values, tzinfo tz):
     """
     Vectorized analogue to pd.Timestamp(value, tz=tz)
diff --git a/pandas/_libs/tslibs/parsing.pyi b/pandas/_libs/tslibs/parsing.pyi
index c7244447edaf7..2e666249a76fc 100644
--- a/pandas/_libs/tslibs/parsing.pyi
+++ b/pandas/_libs/tslibs/parsing.pyi
@@ -40,7 +40,6 @@ def try_parse_datetime_components(
     minutes: npt.NDArray[np.object_],  # object[:]
     seconds: npt.NDArray[np.object_],  # object[:]
 ) -> npt.NDArray[np.object_]: ...
-def format_is_iso(f: str) -> bool: ...
 def guess_datetime_format(
     dt_str,
     dayfirst: bool | None = ...,
diff --git a/pandas/_libs/tslibs/parsing.pyx b/pandas/_libs/tslibs/parsing.pyx
index 26317da62c8d9..aa95febfc9721 100644
--- a/pandas/_libs/tslibs/parsing.pyx
+++ b/pandas/_libs/tslibs/parsing.pyx
@@ -818,26 +818,6 @@ class _timelex:
 _DATEUTIL_LEXER_SPLIT = _timelex.split
 
 
-def format_is_iso(f: str) -> bint:
-    """
-    Does format match the iso8601 set that can be handled by the C parser?
-    Generally of form YYYY-MM-DDTHH:MM:SS - date separator can be different
-    but must be consistent.  Leading 0s in dates and times are optional.
-    """
-    iso_template = "%Y{date_sep}%m{date_sep}%d{time_sep}%H:%M:%S{micro_or_tz}".format
-    excluded_formats = ["%Y%m%d", "%Y%m", "%Y"]
-
-    for date_sep in [" ", "/", "\\", "-", ".", ""]:
-        for time_sep in [" ", "T"]:
-            for micro_or_tz in ["", "%z", ".%f", ".%f%z"]:
-                if (iso_template(date_sep=date_sep,
-                                 time_sep=time_sep,
-                                 micro_or_tz=micro_or_tz,
-                                 ).startswith(f) and f not in excluded_formats):
-                    return True
-    return False
-
-
 def guess_datetime_format(dt_str: str, bint dayfirst=False) -> str | None:
     """
     Guess the datetime format of a given datetime string.
diff --git a/pandas/_libs/tslibs/strptime.pxd b/pandas/_libs/tslibs/strptime.pxd
new file mode 100644
index 0000000000000..175195d4362e4
--- /dev/null
+++ b/pandas/_libs/tslibs/strptime.pxd
@@ -0,0 +1,4 @@
+from numpy cimport int64_t
+
+
+cdef bint parse_today_now(str val, int64_t* iresult, bint utc)
diff --git a/pandas/_libs/tslibs/strptime.pyx b/pandas/_libs/tslibs/strptime.pyx
index a863824d92cc7..27e99706137b6 100644
--- a/pandas/_libs/tslibs/strptime.pyx
+++ b/pandas/_libs/tslibs/strptime.pyx
@@ -34,12 +34,14 @@ from pandas._libs.tslibs.nattype cimport (
     c_nat_strings as nat_strings,
 )
 from pandas._libs.tslibs.np_datetime cimport (
+    NPY_DATETIMEUNIT,
     NPY_FR_ns,
     check_dts_bounds,
     npy_datetimestruct,
     npy_datetimestruct_to_datetime,
     pydate_to_dt64,
     pydatetime_to_dt64,
+    string_to_dts,
 )
 from pandas._libs.tslibs.np_datetime import OutOfBoundsDatetime
 from pandas._libs.tslibs.timestamps cimport _Timestamp
@@ -48,9 +50,50 @@ from pandas._libs.util cimport (
     is_float_object,
     is_integer_object,
 )
+from pandas._libs.tslibs.timestamps import Timestamp
 
 cnp.import_array()
 
+cdef bint format_is_iso(f: str):
+    """
+    Does format match the iso8601 set that can be handled by the C parser?
+    Generally of form YYYY-MM-DDTHH:MM:SS - date separator can be different
+    but must be consistent.  Leading 0s in dates and times are optional.
+    """
+    excluded_formats = ["%Y%m"]
+
+    for date_sep in [" ", "/", "\\", "-", ".", ""]:
+        for time_sep in [" ", "T"]:
+            for micro_or_tz in ["", "%z", ".%f", ".%f%z"]:
+                iso_fmt = f"%Y{date_sep}%m{date_sep}%d{time_sep}%H:%M:%S{micro_or_tz}"
+                if iso_fmt.startswith(f) and f not in excluded_formats:
+                    return True
+    return False
+
+
+def _test_format_is_iso(f: str) -> bool:
+    """Only used in testing."""
+    return format_is_iso(f)
+
+
+cdef bint parse_today_now(str val, int64_t* iresult, bint utc):
+    # We delay this check for as long as possible
+    # because it catches relatively rare cases
+
+    # Multiply by 1000 to convert to nanos, since these methods naturally have
+    #  microsecond resolution
+    if val == "now":
+        if utc:
+            iresult[0] = Timestamp.utcnow().value * 1000
+        else:
+            # GH#18705 make sure to_datetime("now") matches Timestamp("now")
+            # Note using Timestamp.now() is faster than Timestamp("now")
+            iresult[0] = Timestamp.now().value * 1000
+        return True
+    elif val == "today":
+        iresult[0] = Timestamp.today().value * 1000
+        return True
+    return False
 
 cdef dict _parse_code_table = {"y": 0,
                                "Y": 1,
@@ -111,6 +154,9 @@ def array_strptime(
         bint found_naive = False
         bint found_tz = False
         tzinfo tz_out = None
+        bint iso_format = fmt is not None and format_is_iso(fmt)
+        NPY_DATETIMEUNIT out_bestunit
+        int out_local = 0, out_tzoffset = 0
 
     assert is_raise or is_ignore or is_coerce
 
@@ -232,6 +278,34 @@ def array_strptime(
             else:
                 val = str(val)
 
+            if iso_format:
+                string_to_dts_failed = string_to_dts(
+                    val, &dts, &out_bestunit, &out_local,
+                    &out_tzoffset, False, fmt, exact
+                )
+                if not string_to_dts_failed:
+                    # No error reported by string_to_dts, pick back up
+                    # where we left off
+                    value = npy_datetimestruct_to_datetime(NPY_FR_ns, &dts)
+                    if out_local == 1:
+                        # Store the out_tzoffset in seconds
+                        # since we store the total_seconds of
+                        # dateutil.tz.tzoffset objects
+                        tz = timezone(timedelta(minutes=out_tzoffset))
+                        result_timezone[i] = tz
+                        out_local = 0
+                        out_tzoffset = 0
+                    iresult[i] = value
+                    check_dts_bounds(&dts)
+                    continue
+
+            if parse_today_now(val, &iresult[i], utc):
+                continue
+
+            # Some ISO formats can't be parsed by string_to_dts
+            # For example, 6-digit YYYYMD. So, if there's an error,
+            # try the string-matching code below.
+
             # exact matching
             if exact:
                 found = format_regex.match(val)
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index 0162f54bf5225..608b38765621b 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -2118,10 +2118,7 @@ def objects_to_datetime64ns(
     yearfirst,
     utc: bool = False,
     errors: DateTimeErrorChoices = "raise",
-    require_iso8601: bool = False,
     allow_object: bool = False,
-    format: str | None = None,
-    exact: bool = True,
 ):
     """
     Convert data to array of timestamps.
@@ -2134,7 +2131,6 @@ def objects_to_datetime64ns(
     utc : bool, default False
         Whether to convert/localize timestamps to UTC.
     errors : {'raise', 'ignore', 'coerce'}
-    require_iso8601 : bool, default False
     allow_object : bool
         Whether to return an object-dtype ndarray instead of raising if the
         data contains more than one timezone.
@@ -2165,9 +2161,6 @@ def objects_to_datetime64ns(
             utc=utc,
             dayfirst=dayfirst,
             yearfirst=yearfirst,
-            require_iso8601=require_iso8601,
-            format=format,
-            exact=exact,
         )
         result = result.reshape(data.shape, order=order)
     except OverflowError as err:
diff --git a/pandas/core/tools/datetimes.py b/pandas/core/tools/datetimes.py
index a97a866a8406e..49661bd86b7cc 100644
--- a/pandas/core/tools/datetimes.py
+++ b/pandas/core/tools/datetimes.py
@@ -36,7 +36,6 @@
 from pandas._libs.tslibs.conversion import precision_from_unit
 from pandas._libs.tslibs.parsing import (
     DateParseError,
-    format_is_iso,
     guess_datetime_format,
 )
 from pandas._libs.tslibs.strptime import array_strptime
@@ -419,7 +418,6 @@ def _convert_listlike_datetimes(
 
     # warn if passing timedelta64, raise for PeriodDtype
     # NB: this must come after unit transformation
-    orig_arg = arg
     try:
         arg, _ = maybe_convert_dtype(arg, copy=False, tz=libtimezones.maybe_get_tz(tz))
     except TypeError:
@@ -432,24 +430,12 @@ def _convert_listlike_datetimes(
         raise
 
     arg = ensure_object(arg)
-    require_iso8601 = False
 
     if format is None:
         format = _guess_datetime_format_for_array(arg, dayfirst=dayfirst)
 
-    # There is a special fast-path for iso8601 formatted datetime strings
-    require_iso8601 = format is not None and format_is_iso(format)
-
-    if format is not None and not require_iso8601:
-        return _to_datetime_with_format(
-            arg,
-            orig_arg,
-            name,
-            utc,
-            format,
-            exact,
-            errors,
-        )
+    if format is not None:
+        return _array_strptime_with_fallback(arg, name, utc, format, exact, errors)
 
     result, tz_parsed = objects_to_datetime64ns(
         arg,
@@ -457,10 +443,7 @@ def _convert_listlike_datetimes(
         yearfirst=yearfirst,
         utc=utc,
         errors=errors,
-        require_iso8601=require_iso8601,
         allow_object=True,
-        format=format,
-        exact=exact,
     )
 
     if tz_parsed is not None:
@@ -490,40 +473,6 @@ def _array_strptime_with_fallback(
     return _box_as_indexlike(result, utc=utc, name=name)
 
 
-def _to_datetime_with_format(
-    arg,
-    orig_arg,
-    name,
-    utc: bool,
-    fmt: str,
-    exact: bool,
-    errors: str,
-) -> Index:
-    """
-    Try parsing with the given format.
-    """
-    result = None
-
-    # shortcut formatting here
-    if fmt == "%Y%m%d":
-        # pass orig_arg as float-dtype may have been converted to
-        # datetime64[ns]
-        orig_arg = ensure_object(orig_arg)
-        try:
-            # may return None without raising
-            result = _attempt_YYYYMMDD(orig_arg, errors=errors)
-        except (ValueError, TypeError, OutOfBoundsDatetime) as err:
-            raise ValueError(
-                "cannot convert the input to '%Y%m%d' date format"
-            ) from err
-        if result is not None:
-            return _box_as_indexlike(result, utc=utc, name=name)
-
-    # fallback
-    res = _array_strptime_with_fallback(arg, name, utc, fmt, exact, errors)
-    return res
-
-
 def _to_datetime_with_unit(arg, unit, name, utc: bool, errors: str) -> Index:
     """
     to_datetime specalized to the case where a 'unit' is passed.
@@ -978,7 +927,7 @@ def to_datetime(
     in addition to forcing non-dates (or non-parseable dates) to :const:`NaT`.
 
     >>> pd.to_datetime('13000101', format='%Y%m%d', errors='ignore')
-    datetime.datetime(1300, 1, 1, 0, 0)
+    '13000101'
     >>> pd.to_datetime('13000101', format='%Y%m%d', errors='coerce')
     NaT
 
@@ -1011,14 +960,12 @@ def to_datetime(
     Index([2020-10-25 02:00:00+02:00, 2020-10-25 04:00:00+01:00],
           dtype='object')
 
-    - A mix of timezone-aware and timezone-naive inputs is converted to
-      a timezone-aware :class:`DatetimeIndex` if the offsets of the timezone-aware
-      are constant:
+    - A mix of timezone-aware and timezone-naive inputs is also converted to
+      a simple :class:`Index` containing :class:`datetime.datetime` objects:
 
     >>> from datetime import datetime
     >>> pd.to_datetime(["2020-01-01 01:00:00-01:00", datetime(2020, 1, 1, 3, 0)])
-    DatetimeIndex(['2020-01-01 01:00:00-01:00', '2020-01-01 02:00:00-01:00'],
-                  dtype='datetime64[ns, UTC-01:00]', freq=None)
+    Index([2020-01-01 01:00:00-01:00, 2020-01-01 03:00:00], dtype='object')
 
     |
 
diff --git a/pandas/tests/tools/test_to_datetime.py b/pandas/tests/tools/test_to_datetime.py
index 8d001935c97f9..a0667899840f1 100644
--- a/pandas/tests/tools/test_to_datetime.py
+++ b/pandas/tests/tools/test_to_datetime.py
@@ -131,8 +131,11 @@ def test_to_datetime_format_YYYYMMDD_with_nat(self, cache):
         # string with NaT
         ser2 = ser.apply(str)
         ser2[2] = "nat"
-        result = to_datetime(ser2, format="%Y%m%d", cache=cache)
-        tm.assert_series_equal(result, expected)
+        with pytest.raises(
+            ValueError, match='unconverted data remains: ".0", at position 0'
+        ):
+            # https://github.com/pandas-dev/pandas/issues/50051
+            to_datetime(ser2, format="%Y%m%d", cache=cache)
 
     def test_to_datetime_format_YYYYMM_with_nat(self, cache):
         # https://github.com/pandas-dev/pandas/issues/50237
@@ -147,15 +150,26 @@ def test_to_datetime_format_YYYYMM_with_nat(self, cache):
 
     def test_to_datetime_format_YYYYMMDD_ignore(self, cache):
         # coercion
-        # GH 7930
+        # GH 7930, GH 14487
         ser = Series([20121231, 20141231, 99991231])
         result = to_datetime(ser, format="%Y%m%d", errors="ignore", cache=cache)
         expected = Series(
-            [datetime(2012, 12, 31), datetime(2014, 12, 31), datetime(9999, 12, 31)],
+            [20121231, 20141231, 99991231],
             dtype=object,
         )
         tm.assert_series_equal(result, expected)
 
+    def test_to_datetime_format_YYYYMMDD_ignore_with_outofbounds(self, cache):
+        # https://github.com/pandas-dev/pandas/issues/26493
+        result = to_datetime(
+            ["15010101", "20150101", np.nan],
+            format="%Y%m%d",
+            errors="ignore",
+            cache=cache,
+        )
+        expected = Index(["15010101", "20150101", np.nan])
+        tm.assert_index_equal(result, expected)
+
     def test_to_datetime_format_YYYYMMDD_coercion(self, cache):
         # coercion
         # GH 7930
@@ -549,6 +563,26 @@ def test_to_datetime_mixed_date_and_string(self, format):
                 ),
                 id="all tz-aware, mixed offsets, with utc",
             ),
+            pytest.param(
+                False,
+                ["2000-01-01 01:00:00", "2000-01-01 02:00:00+00:00"],
+                Index(
+                    [
+                        Timestamp("2000-01-01 01:00:00"),
+                        Timestamp("2000-01-01 02:00:00+0000", tz="UTC"),
+                    ],
+                ),
+                id="tz-aware string, naive pydatetime, without utc",
+            ),
+            pytest.param(
+                True,
+                ["2000-01-01 01:00:00", "2000-01-01 02:00:00+00:00"],
+                DatetimeIndex(
+                    ["2000-01-01 01:00:00+00:00", "2000-01-01 02:00:00+00:00"],
+                    dtype="datetime64[ns, UTC]",
+                ),
+                id="tz-aware string, naive pydatetime, with utc",
+            ),
         ],
     )
     @pytest.mark.parametrize(
@@ -559,6 +593,7 @@ def test_to_datetime_mixed_datetime_and_string_with_format(
         self, fmt, utc, args, expected, constructor
     ):
         # https://github.com/pandas-dev/pandas/issues/49298
+        # https://github.com/pandas-dev/pandas/issues/50254
         # note: ISO8601 formats go down a fastpath, so we need to check both
         # a ISO8601 format and a non-ISO8601 one
         ts1 = constructor(args[0])
@@ -566,6 +601,62 @@ def test_to_datetime_mixed_datetime_and_string_with_format(
         result = to_datetime([ts1, ts2], format=fmt, utc=utc)
         tm.assert_index_equal(result, expected)
 
+    @pytest.mark.parametrize(
+        "fmt, utc, expected",
+        [
+            pytest.param(
+                "%Y-%m-%d %H:%M:%S%z",
+                True,
+                DatetimeIndex(
+                    ["2000-01-01 08:00:00+00:00", "2000-01-02 00:00:00+00:00", "NaT"],
+                    dtype="datetime64[ns, UTC]",
+                ),
+                id="ISO8601, UTC",
+            ),
+            pytest.param(
+                "%Y-%m-%d %H:%M:%S%z",
+                False,
+                Index(
+                    [
+                        Timestamp("2000-01-01 09:00:00+0100", tz="UTC+01:00"),
+                        Timestamp("2000-01-02 02:00:00+0200", tz="UTC+02:00"),
+                        NaT,
+                    ]
+                ),
+                id="ISO8601, non-UTC",
+            ),
+            pytest.param(
+                "%Y-%d-%m %H:%M:%S%z",
+                True,
+                DatetimeIndex(
+                    ["2000-01-01 08:00:00+00:00", "2000-02-01 00:00:00+00:00", "NaT"],
+                    dtype="datetime64[ns, UTC]",
+                ),
+                id="non-ISO8601, UTC",
+            ),
+            pytest.param(
+                "%Y-%d-%m %H:%M:%S%z",
+                False,
+                Index(
+                    [
+                        Timestamp("2000-01-01 09:00:00+0100", tz="UTC+01:00"),
+                        Timestamp("2000-02-01 02:00:00+0200", tz="UTC+02:00"),
+                        NaT,
+                    ]
+                ),
+                id="non-ISO8601, non-UTC",
+            ),
+        ],
+    )
+    def test_to_datetime_mixed_offsets_with_none(self, fmt, utc, expected):
+        # https://github.com/pandas-dev/pandas/issues/50071
+        result = to_datetime(
+            ["2000-01-01 09:00:00+01:00", "2000-01-02 02:00:00+02:00", None],
+            format=fmt,
+            utc=utc,
+        )
+        tm.assert_index_equal(result, expected)
+
     @pytest.mark.parametrize(
         "fmt",
         ["%Y-%d-%m %H:%M:%S%z", "%Y-%m-%d %H:%M:%S%z"],
@@ -835,6 +926,29 @@ def test_to_datetime_today(self, tz):
     def test_to_datetime_today_now_unicode_bytes(self, arg):
         to_datetime([arg])
 
+    @pytest.mark.parametrize(
+        "format, expected_ds",
+        [
+            ("%Y-%m-%d %H:%M:%S%z", "2020-01-03"),
+            ("%Y-%d-%m %H:%M:%S%z", "2020-03-01"),
+            (None, "2020-01-03"),
+        ],
+    )
+    @pytest.mark.parametrize(
+        "string, attribute",
+        [
+            ("now", "utcnow"),
+            ("today", "today"),
+        ],
+    )
+    def test_to_datetime_now_with_format(self, format, expected_ds, string, attribute):
+        # https://github.com/pandas-dev/pandas/issues/50359
+        result = to_datetime(["2020-01-03 00:00:00Z", string], format=format, utc=True)
+        expected = DatetimeIndex(
+            [expected_ds, getattr(Timestamp, attribute)()], dtype="datetime64[ns, UTC]"
+        )
+        assert (expected - result).max().total_seconds() < 1
+
     @pytest.mark.parametrize(
         "dt", [np.datetime64("2000-01-01"), np.datetime64("2000-01-02")]
     )
@@ -2004,12 +2118,15 @@ def test_to_datetime_iso8601_fails(self, input, format, exact):
     def test_to_datetime_iso8601_exact_fails(self, input, format):
         # https://github.com/pandas-dev/pandas/issues/12649
         # `format` is shorter than the date string, so only fails with `exact=True`
+        msg = "|".join(
+            [
+                '^unconverted data remains: ".*", at position 0$',
+                'time data ".*" doesn\'t match format ".*", at position 0',
+            ]
+        )
         with pytest.raises(
             ValueError,
-            match=(
-                rf"time data \"{input}\" doesn't match format "
-                rf"\"{format}\", at position 0"
-            ),
+            match=(msg),
         ):
             to_datetime(input, format=format)
 
@@ -2074,6 +2191,28 @@ def test_to_datetime_iso8601_valid(self, input, format):
         result = to_datetime(input, format=format)
         assert result == expected
 
+    @pytest.mark.parametrize(
+        "input, format",
+        [
+            ("2020-1", "%Y-%m"),
+            ("2020-1-1", "%Y-%m-%d"),
+            ("2020-1-1 0", "%Y-%m-%d %H"),
+            ("2020-1-1T0", "%Y-%m-%dT%H"),
+            ("2020-1-1 0:0", "%Y-%m-%d %H:%M"),
+            ("2020-1-1T0:0", "%Y-%m-%dT%H:%M"),
+            ("2020-1-1 0:0:0", "%Y-%m-%d %H:%M:%S"),
+            ("2020-1-1T0:0:0", "%Y-%m-%dT%H:%M:%S"),
+            ("2020-1-1T0:0:0.000", "%Y-%m-%dT%H:%M:%S.%f"),
+            ("2020-1-1T0:0:0.000000", "%Y-%m-%dT%H:%M:%S.%f"),
+            ("2020-1-1T0:0:0.000000000", "%Y-%m-%dT%H:%M:%S.%f"),
+        ],
+    )
+    def test_to_datetime_iso8601_non_padded(self, input, format):
+        # https://github.com/pandas-dev/pandas/issues/21422
+        expected = Timestamp(2020, 1, 1)
+        result = to_datetime(input, format=format)
+        assert result == expected
+
     @pytest.mark.parametrize(
         "input, format",
         [
@@ -2587,8 +2726,7 @@ def test_day_not_in_month_raise(self, cache):
             (
                 "2015-02-29",
                 "%Y-%m-%d",
-                '^time data "2015-02-29" doesn\'t match format "%Y-%m-%d", '
-                "at position 0$",
+                "^day is out of range for month, at position 0$",
             ),
             (
                 "2015-29-02",
@@ -2598,8 +2736,7 @@ def test_day_not_in_month_raise(self, cache):
             (
                 "2015-02-32",
                 "%Y-%m-%d",
-                '^time data "2015-02-32" doesn\'t match format "%Y-%m-%d", '
-                "at position 0$",
+                '^unconverted data remains: "2", at position 0$',
             ),
             (
                 "2015-32-02",
@@ -2610,8 +2747,7 @@ def test_day_not_in_month_raise(self, cache):
             (
                 "2015-04-31",
                 "%Y-%m-%d",
-                '^time data "2015-04-31" doesn\'t match format "%Y-%m-%d", '
-                "at position 0$",
+                "^day is out of range for month, at position 0$",
             ),
             (
                 "2015-31-04",
diff --git a/pandas/tests/tslibs/test_parsing.py b/pandas/tests/tslibs/test_parsing.py
index 7675305e27d22..558c802fd70f6 100644
--- a/pandas/tests/tslibs/test_parsing.py
+++ b/pandas/tests/tslibs/test_parsing.py
@@ -8,7 +8,10 @@
 import numpy as np
 import pytest
 
-from pandas._libs.tslibs import parsing
+from pandas._libs.tslibs import (
+    parsing,
+    strptime,
+)
 from pandas._libs.tslibs.parsing import parse_time_string
 import pandas.util._test_decorators as td
 
@@ -154,27 +157,25 @@ def test_parsers_month_freq(date_str, expected):
         ("2011-12-30T00:00:00", "%Y-%m-%dT%H:%M:%S"),
         ("2011-12-30T00:00:00UTC", "%Y-%m-%dT%H:%M:%S%Z"),
         ("2011-12-30T00:00:00Z", "%Y-%m-%dT%H:%M:%S%z"),
-        # The +9 format for offsets is supported by dateutil,
-        # but don't round-trip, see https://github.com/pandas-dev/pandas/issues/48921
-        ("2011-12-30T00:00:00+9", None),
-        ("2011-12-30T00:00:00+09", None),
+        ("2011-12-30T00:00:00+9", "%Y-%m-%dT%H:%M:%S%z"),
+        ("2011-12-30T00:00:00+09", "%Y-%m-%dT%H:%M:%S%z"),
         ("2011-12-30T00:00:00+090", None),
         ("2011-12-30T00:00:00+0900", "%Y-%m-%dT%H:%M:%S%z"),
         ("2011-12-30T00:00:00-0900", "%Y-%m-%dT%H:%M:%S%z"),
         ("2011-12-30T00:00:00+09:00", "%Y-%m-%dT%H:%M:%S%z"),
         ("2011-12-30T00:00:00+09:000", None),
-        ("2011-12-30T00:00:00+9:0", None),
+        ("2011-12-30T00:00:00+9:0", "%Y-%m-%dT%H:%M:%S%z"),
         ("2011-12-30T00:00:00+09:", None),
         ("2011-12-30T00:00:00.000000UTC", "%Y-%m-%dT%H:%M:%S.%f%Z"),
         ("2011-12-30T00:00:00.000000Z", "%Y-%m-%dT%H:%M:%S.%f%z"),
-        ("2011-12-30T00:00:00.000000+9", None),
-        ("2011-12-30T00:00:00.000000+09", None),
+        ("2011-12-30T00:00:00.000000+9", "%Y-%m-%dT%H:%M:%S.%f%z"),
+        ("2011-12-30T00:00:00.000000+09", "%Y-%m-%dT%H:%M:%S.%f%z"),
         ("2011-12-30T00:00:00.000000+090", None),
         ("2011-12-30T00:00:00.000000+0900", "%Y-%m-%dT%H:%M:%S.%f%z"),
         ("2011-12-30T00:00:00.000000-0900", "%Y-%m-%dT%H:%M:%S.%f%z"),
         ("2011-12-30T00:00:00.000000+09:00", "%Y-%m-%dT%H:%M:%S.%f%z"),
         ("2011-12-30T00:00:00.000000+09:000", None),
-        ("2011-12-30T00:00:00.000000+9:0", None),
+        ("2011-12-30T00:00:00.000000+9:0", "%Y-%m-%dT%H:%M:%S.%f%z"),
         ("2011-12-30T00:00:00.000000+09:", None),
         ("2011-12-30 00:00:00.000000", "%Y-%m-%d %H:%M:%S.%f"),
         ("Tue 24 Aug 2021 01:30:48 AM", "%a %d %b %Y %H:%M:%S %p"),
@@ -305,16 +306,16 @@ def test_parse_time_string_check_instance_type_raise_exception():
         ("%Y-%m-%dT%H:%M:%S.%f", True),
         ("%Y-%m-%dT%H:%M:%S.%f%z", True),
         ("%Y-%m-%dT%H:%M:%S.%f%Z", False),
-        ("%Y%m%d", False),
+        ("%Y%m%d", True),
         ("%Y%m", False),
-        ("%Y", False),
+        ("%Y", True),
         ("%Y-%m-%d", True),
         ("%Y-%m", True),
     ],
 )
 def test_is_iso_format(fmt, expected):
     # see gh-41047
-    result = parsing.format_is_iso(fmt)
+    result = strptime._test_format_is_iso(fmt)
     assert result == expected