diff --git a/NAMESPACE b/NAMESPACE
index 27aa1805f0..249f2b2d55 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -8,7 +8,8 @@ exportClasses(data.table, IDate, ITime)
 export(data.table, tables, setkey, setkeyv, key, "key<-", haskey, CJ, SJ, copy)
 export(setindex, setindexv, indices)
 export(set2key, set2keyv, key2) # deprecated with helpful error; remove after May 2019 (see #3399)
-export(as.data.table,is.data.table,test.data.table,last,first,like,"%like%",between,"%between%",inrange,"%inrange%")
+export(as.data.table,is.data.table,test.data.table)
+export(last,first,like,"%like%","%ilike%","%flike%",between,"%between%",inrange,"%inrange%")
 export(timetaken)
 export(truelength, alloc.col, ":=")
 export(setattr, setnames, setcolorder, set, setDT, setDF)
diff --git a/NEWS.md b/NEWS.md
index d803be59ac..e7f3eb0ba1 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -75,6 +75,8 @@
 
 8. `between()` and `%between%` are faster for `POSIXct`, [#3519](https://github.com/Rdatatable/data.table/issues/3519), and now support the `.()` alias, [#2315](https://github.com/Rdatatable/data.table/issues/2315). Thanks to @Henrik-P for the reports. There is now also support for `bit64`'s `integer64` class and more robust coercion of types, [#3517](https://github.com/Rdatatable/data.table/issues/3517).
 
+9. New convenience functions `%ilike%` and `%flike%` which map to new `like()` arguments `ignore.case` and `fixed` respectively, [#3333](https://github.com/Rdatatable/data.table/issues/3333). `%ilike%` is for case-insensitive pattern matching. `%flike%` is for more efficient matching of fixed strings. Thanks to @andreasLD for providing most of the core code.
+
 #### 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/like.R b/R/like.R
index c19c8791e7..393853be01 100644
--- a/R/like.R
+++ b/R/like.R
@@ -1,16 +1,18 @@
-like <- function(vector, pattern)
-{
-  # Intended for use with a data.table 'where'
-  # Don't use * or % like SQL's like.  Uses regexpr syntax - more powerful.
+# Intended for use with a data.table 'where'
+# Don't use * or % like SQL's like.  Uses regexpr syntax - more powerful.
+# returns 'logical' so can be combined with other where clauses.
+like <- function(vector, pattern, ignore.case = FALSE, fixed = FALSE) {
   if (is.factor(vector)) {
-    as.integer(vector) %in% grep(pattern,levels(vector))
+    as.integer(vector) %in% grep(pattern, levels(vector), ignore.case = ignore.case, fixed = fixed)
   } else {
     # most usually character, but integer and numerics will be silently coerced by grepl
-    grepl(pattern,vector)
+    grepl(pattern, vector, ignore.case = ignore.case, fixed = fixed)
   }
-  # returns 'logical' so can be combined with other where clauses.
 }
 
-"%like%" = like
-
-
+"%like%" = function(vector, pattern) like(vector, pattern)
+# as grep -i -- grep, ignoring case
+"%ilike%" = function(vector, pattern) like(vector, pattern, ignore.case = TRUE)
+# as grep -F or fgrep -- grep against a fixed pattern (no regex)
+#   (more efficient where applicable)
+"%flike%" = function(vector, pattern) like(vector, pattern, fixed = TRUE)
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index 04b85b889a..749fd54f9c 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -7117,7 +7117,7 @@ test(1530.2, which.first(x), which(x)[1L])
 test(1530.3, which.last(1:5), error = "x not boolean")
 test(1530.4, which.last(x), tail(which(x), 1L))
 
-# test for like, %like%
+# test for like, %like%, %ilike%, %flike%
 set.seed(2L)
 x = apply(matrix(sample(letters, 12), nrow=2), 1, paste, collapse="")
 y = factor(sample(c(letters[1:5], x), 20, TRUE))
@@ -7126,6 +7126,13 @@ test(1532.1, y %like% xsub[1L], grepl(xsub[1L], y))
 test(1532.2, y %like% xsub[2L], grepl(xsub[2L], y))
 test(1532.3, like(y, xsub[1L]), grepl(xsub[1L], y))
 test(1532.4, like(y, xsub[2L]), grepl(xsub[2L], y))
+## %ilike% and %flike% for #3333
+x = c('HEY', 'hey', '()')
+test(1532.5, like(x, 'hey', ignore.case = TRUE), c(TRUE, TRUE, FALSE))
+test(1532.6, like(x, '()'), c(TRUE, TRUE, TRUE))
+test(1532.7, like(x, '()', fixed = TRUE), c(FALSE, FALSE, TRUE))
+test(1532.8, x %ilike% 'hey', c(TRUE, TRUE, FALSE))
+test(1532.9, x %flike% '()', c(FALSE, FALSE, TRUE))
 
 # coverage for setkey() to 100%
 dt1 = data.table(x=sample(5), y=1:5, key="y")
diff --git a/man/like.Rd b/man/like.Rd
index 22f88f706c..de6edae0fd 100644
--- a/man/like.Rd
+++ b/man/like.Rd
@@ -1,27 +1,38 @@
 \name{like}
 \alias{like}
 \alias{\%like\%}
-\title{ Convenience function for calling regexpr. }
+\alias{\%ilike\%}
+\alias{\%flike\%}
+\title{ Convenience function for calling grep. }
 \description{
-  Intended for use in \code{i} in \code{[.data.table}.
+  Intended for use in \code{i} in \code{\link[=data.table]{[.data.table}}, i.e., for subsetting/filtering.
+  
+  Syntax should be familiar to SQL users, with interpretation as regex.
 }
 \usage{
-like(vector,pattern)
+like(vector, pattern, ignore.case = FALSE, fixed = FALSE)
 vector \%like\% pattern
+vector \%ilike\% pattern
+vector \%flike\% pattern
 }
 \arguments{
-   \item{vector}{ Either a \code{character} vector or a \code{factor}. A \code{factor} is faster. }
-   \item{pattern}{ Passed on to \code{\link{grepl}}. }
+   \item{vector}{ Either a \code{character} or a \code{factor} vector. }
+   \item{pattern}{ Pattern to be matched }
+   \item{ignore.case}{ \code{logical}; is \code{pattern} case-sensitive? }
+   \item{fixed}{ \code{logical}; should \code{pattern} be interpreted as a literal string (i.e., ignoring regular expressions)? }
+}
+\details{
+  Internally, \code{like} is essentially a wrapper around \code{\link[base]{grepl}}, except that it is smarter about handling \code{factor} input (\code{base::grep} uses slow \code{as.character} conversion).
 }
-% \details{
-% }
 \value{
     Logical vector, \code{TRUE} for items that match \code{pattern}.
 }
 \note{ Current implementation does not make use of sorted keys. }
-\seealso{ \code{\link{data.table}}, \code{\link{grepl}} }
+\seealso{ \code{\link[base]{grepl}} }
 \examples{
 DT = data.table(Name=c("Mary","George","Martha"), Salary=c(2,3,4))
 DT[Name \%like\% "^Mar"]
+DT[Name \%ilike\% "mar"]
+DT[Name \%flike\% "Mar"]
 }
 \keyword{ data }