diff --git a/NAMESPACE b/NAMESPACE
index cb45cf86f..d6abdde07 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -163,6 +163,14 @@ S3method(split, IDate)
 S3method(unique, IDate)
 S3method(unique, ITime)
 
+# generic to support custom column formatters
+export(format_col)
+S3method(format_col, default)
+S3method(format_col, POSIXct)
+S3method(format_col, expression)
+export(format_list_item)
+S3method(format_list_item, default)
+
 # duplist
 # getdots
 # NCOL
diff --git a/NEWS.md b/NEWS.md
index 478ffb855..e8dc4d192 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -71,6 +71,8 @@
 
 7. New variable `.Last.updated` (similar to R's `.Last.value`) contains the number of rows affected by the most recent `:=` or `set()`, [#1885](https://github.com/Rdatatable/data.table/issues/1885).
 
+8. `data.table` printing now supports customizable methods for both columns and list column row items, part of [#1523](https://github.com/Rdatatable/data.table/issues/1523). `format_col` is S3-generic for customizing how to print whole columns; `format_list_item` is S3-generic for customizing how to print each row of a list column. Thanks variously to @mllg, who initially filed [#3338](https://github.com/Rdatatable/data.table/pulls/3338) with the seed of the idea, @franknarf1 who earlier suggested the idea of providing custom formatters, @fparages who submitted a patch to improve the printing of timezones for [#2842](https://github.com/Rdatatable/data.table/issues/2842), @RichardRedding for pointing out an error relating to printing wide `expression` columns in [#3011](https://github.com/Rdatatable/data.table/issues/3011), and @MichaelChirico for the ultimate implementation. See `?print.data.table` for examples.
+
 #### BUG FIXES
 
 1. `first`, `last`, `head` and `tail` by group no longer error in some cases, [#2030](https://github.com/Rdatatable/data.table/issues/2030) [#3462](https://github.com/Rdatatable/data.table/issues/3462). Thanks to @franknarf1 for reporting.
diff --git a/R/print.data.table.R b/R/print.data.table.R
index 6edf0d195..8bd10735b 100644
--- a/R/print.data.table.R
+++ b/R/print.data.table.R
@@ -6,8 +6,7 @@ print.data.table <- function(x, topn=getOption("datatable.print.topn"),
                row.names=getOption("datatable.print.rownames"),
                col.names=getOption("datatable.print.colnames"),
                print.keys=getOption("datatable.print.keys"),
-               quote=FALSE,
-               timezone=FALSE, ...) {    
+               quote=FALSE, ...) {    
   # topn  - print the top topn and bottom topn rows with '---' inbetween (5)
   # nrows - under this the whole (small) table is printed, unless topn is provided (100)
   # class - should column class be printed underneath column name? (FALSE)
@@ -64,7 +63,7 @@ print.data.table <- function(x, topn=getOption("datatable.print.topn"),
     rn = seq_len(nrow(x))
     printdots = FALSE
   }
-  toprint=format.data.table(toprint, na.encode=FALSE, timezone = timezone, ...)  # na.encode=FALSE so that NA in character cols print as <NA>
+  toprint=format.data.table(toprint, na.encode=FALSE, ...)  # na.encode=FALSE so that NA in character cols print as <NA>
 
   if ((!"bit64" %chin% loadedNamespaces()) && any(sapply(x,inherits,"integer64"))) require_bit64()
   # When we depend on R 3.2.0 (Apr 2015) we can use isNamespaceLoaded() added then, instead of %chin% above
@@ -111,44 +110,11 @@ print.data.table <- function(x, topn=getOption("datatable.print.topn"),
   invisible(x)
 }
 
-format.data.table <- function (x, ..., justify="none", timezone = FALSE) {
+format.data.table <- function (x, ..., justify="none") {
   if (is.atomic(x) && !is.null(x)) {
     stop("Internal structure doesn't seem to be a list. Possibly corrupt data.table.")
   }
-  format.item <- function(x) {
-    if (is.null(x))  # NULL item in a list column
-      ""
-    else if (is.atomic(x) || inherits(x,"formula")) # FR #2591 - format.data.table issue with columns of class "formula"
-      paste(c(format(head(x, 6L), justify=justify, ...), if (length(x) > 6L) "..."), collapse=",")  # fix for #5435 - format has to be added here...
-    else
-      paste0("<", class(x)[1L], ">")
-  }
-  # FR #2842 add timezone for posix timestamps
-  format.timezone <- function(col) { # paste timezone to a time object
-    tz = attr(col,'tzone', exact = TRUE)
-    if (!is.null(tz)) { # date object with tz
-      nas = is.na(col)
-      col = paste0(as.character(col)," ",tz) # parse to character
-      col[nas] = NA_character_
-    }
-    return(col)
-  }
-  # FR #1091 for pretty printing of character
-  # TODO: maybe instead of doing "this is...", we could do "this ... test"?
-  char.trunc <- function(x, trunc.char = getOption("datatable.prettyprint.char")) {
-    trunc.char = max(0L, suppressWarnings(as.integer(trunc.char[1L])), na.rm=TRUE)
-    if (!is.character(x) || trunc.char <= 0L) return(x)
-    idx = which(nchar(x) > trunc.char)
-    x[idx] = paste0(substr(x[idx], 1L, as.integer(trunc.char)), "...")
-    x
-  }
-  do.call("cbind",lapply(x,function(col,...){
-    if (!is.null(dim(col))) stop("Invalid column: it has dimensions. Can't format it. If it's the result of data.table(table()), use as.data.table(table()) instead.")
-    if(timezone) col = format.timezone(col)
-    if (is.list(col)) col = vapply_1c(col, format.item)
-    else col = format(char.trunc(col), justify=justify, ...) # added an else here to fix #5435
-    col
-  },...))
+  do.call("cbind", lapply(x, format_col, ..., justify=justify))
 }
 
 mimicsAutoPrint = c("knit_print.default")
@@ -165,3 +131,40 @@ shouldPrint = function(x) {
 #   as opposed to printing a blank line, for excluding col.names per PR #1483
 cut_top = function(x) cat(capture.output(x)[-1L], sep = '\n')
 
+format_col = function(x, ...) {
+  UseMethod("format_col")
+}
+
+format_list_item = function(x, ...) {
+  UseMethod("format_list_item")
+}
+
+format_col.default = function(x, ...) {
+  if (!is.null(dim(x))) stop("Invalid column: it has dimensions. Can't format it. If it's the result of data.table(table()), use as.data.table(table()) instead.")
+  if (is.list(x)) return(vapply_1c(x, format_list_item))
+  format(char.trunc(x), ...) # added an else here to fix #5435
+}
+
+# #2842 -- different columns can have different tzone, so force usage in output
+format_col.POSIXct = function(x, ...) format(x, usetz = TRUE, ...)
+
+# #3011 -- expression columns can wrap to newlines which breaks printing
+format_col.expression = function(x, ...) format(char.trunc(as.character(x)), ...)
+
+format_list_item.default = function(x, ...) {
+  if (is.null(x)) return ("") # NULL item in a list column
+  if (is.atomic(x) || inherits(x, "formula")) # FR #2591 - format.data.table issue with columns of class "formula"
+    paste(c(format(head(x, 6L), ...), if (length(x) > 6L) "..."), collapse=",")  # fix for #5435 - format has to be added here...
+  else
+    paste0("<", class(x)[1L], ">")
+}
+
+# FR #1091 for pretty printing of character
+# TODO: maybe instead of doing "this is...", we could do "this ... test"?
+char.trunc <- function(x, trunc.char = getOption("datatable.prettyprint.char")) {
+  trunc.char = max(0L, suppressWarnings(as.integer(trunc.char[1L])), na.rm=TRUE)
+  if (!is.character(x) || trunc.char <= 0L) return(x)
+  idx = which(nchar(x) > trunc.char)
+  x[idx] = paste0(substr(x[idx], 1L, as.integer(trunc.char)), "...")
+  x
+}
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index a3a88f6ef..beb0674dd 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -14178,12 +14178,13 @@ test(2025.11, fread(f), data.table(A=1:2, B=c("foobar","baz"), C=3:4))
 
 # printing timezone, #2842
 DT = data.table(t1 = as.POSIXct("1982-04-26 13:34:56", tz = "Europe/Madrid"),t2 = as.POSIXct("2019-01-01 19:00:01",tz = "UTC"))
-test(2026.1, capture.output(print(DT))[2], "1: 1982-04-26 13:34:56 2019-01-01 19:00:01")
-test(2026.2, capture.output(print(DT,timezone = TRUE))[2], "1: 1982-04-26 13:34:56 Europe/Madrid 2019-01-01 19:00:01 UTC")
-DT = data.table(v1 = c(1,as.numeric(NA)))
-DT[2,t:= as.POSIXct("2019-01-01 19:00:01",tz = "UTC")]
-test(2026.3, capture.output(print(DT)), c("   v1                   t","1:  1                <NA>", "2: NA 2019-01-01 19:00:01"))
-test(2026.4, capture.output(print(DT, timezone = TRUE)), c("   v1                       t","1:  1                    <NA>","2: NA 2019-01-01 19:00:01 UTC"))
+test(2026.1, capture.output(print(DT))[2L], "1: 1982-04-26 13:34:56 CEST 2019-01-01 19:00:01 UTC")
+DT = data.table(v1 = c(1, as.numeric(NA)))
+DT[2L, t:= as.POSIXct("2019-01-01 19:00:01", tz = "UTC")]
+test(2026.2, capture.output(print(DT)),
+     c("   v1                       t",
+       "1:  1                    <NA>", 
+       "2: NA 2019-01-01 19:00:01 UTC"))
 
 # empty item in j=list(x, ) errors gracefully, #3507
 DT = data.table(a = 1:5)
@@ -14405,6 +14406,28 @@ test(2034.1, fread('A,B\n"foo","ba"r"', quote="''"), error='quote= must be a sin
 test(2034.2, fread('A,B\n"foo","ba"r"', quote=FALSE), ans<-data.table(A='"foo"', B='"ba"r"'))
 test(2034.3, fread('A,B\n"foo","ba"r"', quote=""), ans)
 
+# format_col and format_list_item printing helpers/generics
+## Use case: solve #2842 by defining format_col.POSIXct to have usetz = TRUE
+DT = data.table(
+  t1 = as.POSIXct('2018-05-01 12:34:56', tz = 'UTC'),
+  t2 = as.POSIXct('2018-05-01 12:34:56', tz = 'Asia/Singapore')
+)
+test(2035.1, DT, output = 'UTC.*\\+08')
+
+# #3011 -- default expression printing can break format_col.default
+test(2035.2, print(data.table(e = expression(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13))), output = '1 + 2 + 3')
+
+# format_col generic is used
+format_col.complex = function(x, ...) sprintf('(%.1f, %.1fi)', Re(x), Im(x))
+registerS3method("format_col", "complex", format_col.complex)
+x = data.table(z = c(1 + 3i, 2 - 1i, pi + 2.718i))
+test(2035.3, x, output = '(1.0, 3.0i)')
+
+# format_list_item() generic is used
+format_list_item.myclass <- function(x, ...) paste0("<", class(x)[1L], ":", x$id, ">")
+registerS3method("format_list_item", "myclass", format_list_item.myclass)
+DT = data.table(row = 1:2, objs = list(structure(list(id = "foo"), class = "myclass"),  structure(list(id = "bar"), class = "myclass")))
+test(2035.4, print(DT), output = "myclass:foo.*myclass:bar")
 
 ###################################
 #  Add new tests above this line  #
diff --git a/man/print.data.table.Rd b/man/print.data.table.Rd
index 3b7fe7e16..9ba6c712b 100644
--- a/man/print.data.table.Rd
+++ b/man/print.data.table.Rd
@@ -1,10 +1,18 @@
 \name{print.data.table}
 \alias{print.data.table}
+\alias{format_col}
+\alias{format_col.default}
+\alias{format_col.POSIXct}
+\alias{format_col.expression}
+\alias{format_list_item}
+\alias{format_list_item.default}
 \title{ data.table Printing Options }
 \description{
   \code{print.data.table} extends the functionalities of \code{print.data.frame}.
 
   Key enhancements include automatic output compression of many observations and concise column-wise \code{class} summary.
+  
+  \code{format_col} and \code{format_list_item} generics provide flexibility for end-users to define custom printing methods for generic classes.
 }
 \usage{
   \method{print}{data.table}(x,
@@ -14,8 +22,15 @@
     row.names=getOption("datatable.print.rownames"), # default: TRUE
     col.names=getOption("datatable.print.colnames"), # default: "auto"
     print.keys=getOption("datatable.print.keys"),    # default: FALSE
-    quote=FALSE,
-    timezone=FALSE, \dots)
+    quote=FALSE, \dots)
+    
+  format_col(x, \dots)
+  \method{format_col}{default}(x, \dots)
+  \method{format_col}{POSIXct}(x, \dots)
+  \method{format_col}{expression}{x, \dots)
+
+  format_list_item(x, \dots)
+  \method{format_list_item}{default}(x, \dots)
 }
 \arguments{
   \item{x}{ A \code{data.table}. }
@@ -26,11 +41,20 @@
   \item{col.names}{ One of three flavours for controlling the display of column names in output. \code{"auto"} includes column names above the data, as well as below the table if \code{nrow(x) > 20}. \code{"top"} excludes this lower register when applicable, and \code{"none"} suppresses column names altogether (as well as column classes if \code{class = TRUE}. }
   \item{print.keys}{ If \code{TRUE}, any \code{\link{key}} and/or \code{\link[=indices]{index}} currently assigned to \code{x} will be printed prior to the preview of the data. }
   \item{quote}{ If \code{TRUE}, all output will appear in quotes, as in \code{print.default}. }
-  \item{timezone}{ If \code{TRUE}, time columns of class POSIXct or POSIXlt will be printed with their timezones (if attribute is available). }
   \item{\dots}{ Other arguments ultimately passed to \code{format}. }
 }
+\value{
+  \code{print.data.table} returns \code{x} invisibly.
+
+  \code{format_col} returns a \code{length(x)}-size \code{character} vector.
+
+  \code{format_list_item} returns a length-1 \code{character} scalar.
+}
 \details{
   By default, with an eye to the typically large number of observations in a code{data.table}, only the beginning and end of the object are displayed (specifically, \code{head(x, topn)} and \code{tail(x, topn)} are displayed unless \code{nrow(x) < nrows}, in which case all rows will print).
+  
+  \code{format_col} is applied at a column level; for example, \code{format_col.POSIXct} is used to tag the time zones of \code{POSIXct} columns. \code{format_list_item} is applied to the elements (rows) of \code{list} columns; see Examples. 
+
 }
 \seealso{\code{\link{print.default}}}
 \examples{
@@ -58,5 +82,17 @@
   setindexv(DT, c("a", "b"))
   setindexv(DT, "a")
   print(DT, print.keys=TRUE)
-}
+  
+  # Formatting customization
+  format_col.complex = function(x, ...) sprintf('(\%.1f, \%.1fi)', Re(x), Im(x))
+  registerS3method("format_col", "complex", format_col.complex)
+  x = data.table(z = c(1 + 3i, 2 - 1i, pi + 2.718i))
+  print(x)
 
+  iris = as.data.table(iris)
+  iris_agg = iris[ , .(reg = list(lm(Sepal.Length ~ Petal.Length))), by = Species]
+  format_list_item.lm = function(x) sprintf('<lm:\%s>', format(x$call$formula))
+  registerS3method("format_list_item", "lm", format_list_item.lm)
+  print(iris_agg)
+
+}