diff --git a/NEWS.md b/NEWS.md
index e37be8ca5d..36c4af6278 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -59,6 +59,9 @@
 
 * `stat_bin()` now handles data with only one unique value (@yutannihilation #3047).
 
+* `stat_function()` now accepts rlang/purrr style anonymous functions for the 
+  `fun` parameter (@dkahle, #3159).
+
 * `geom_polygon()` can now draw polygons with holes using the new `subgroup` 
   aesthetic. This functionality requires R 3.6 (@thomasp85, #3128)
 
diff --git a/R/stat-function.r b/R/stat-function.r
index 15df7e166e..8c76f8e432 100644
--- a/R/stat-function.r
+++ b/R/stat-function.r
@@ -1,13 +1,16 @@
 #' Compute function for each x value
 #'
-#' This stat makes it easy to superimpose a function on top of an existing
-#' plot. The function is called with a grid of evenly spaced values along
-#' the x axis, and the results are drawn (by default) with a line.
+#' This stat makes it easy to superimpose a function on top of an existing plot.
+#' The function is called with a grid of evenly spaced values along the x axis,
+#' and the results are drawn (by default) with a line.
 #'
 #' @eval rd_aesthetics("stat", "function")
-#' @param fun function to use. Must be vectorised.
-#' @param n number of points to interpolate along
-#' @param args list of additional arguments to pass to `fun`
+#' @param fun Function to use. Either 1) an anonymous function in the base or
+#'   rlang formula syntax (see [rlang::as_function()])
+#'   or 2) a quoted or character name referencing a function; see examples. Must
+#'   be vectorised.
+#' @param n Number of points to interpolate along
+#' @param args List of additional arguments to pass to `fun`
 #' @param xlim Optionally, restrict the range of the function to this range.
 #' @inheritParams layer
 #' @inheritParams geom_point
@@ -16,39 +19,41 @@
 #'   \item{x}{x's along a grid}
 #'   \item{y}{value of function evaluated at corresponding x}
 #' }
+#' @seealso [rlang::as_function()]
 #' @export
 #' @examples
+#'
+#' # stat_function is useful for overlaying functions
 #' set.seed(1492)
-#' df <- data.frame(
-#'   x = rnorm(100)
-#' )
-#' x <- df$x
-#' base <- ggplot(df, aes(x)) + geom_density()
-#' base + stat_function(fun = dnorm, colour = "red")
-#' base + stat_function(fun = dnorm, colour = "red", args = list(mean = 3))
+#' ggplot(data.frame(x = rnorm(100)), aes(x)) +
+#'   geom_density() +
+#'   stat_function(fun = dnorm, colour = "red")
 #'
-#' # Plot functions without data
-#' # Examples adapted from Kohske Takahashi
+#' # To plot functions without data, specify range of x-axis
+#' base <- ggplot(data.frame(x = c(-5, 5)), aes(x))
+#' base + stat_function(fun = dnorm)
+#' base + stat_function(fun = dnorm, args = list(mean = 2, sd = .5))
 #'
-#' # Specify range of x-axis
-#' ggplot(data.frame(x = c(0, 2)), aes(x)) +
-#'   stat_function(fun = exp, geom = "line")
+#' # The underlying mechanics evaluate the function at discrete points
+#' # and connect the points with lines
+#' base <- ggplot(data.frame(x = c(-5, 5)), aes(x))
+#' base + stat_function(fun = dnorm, geom = "point")
+#' base + stat_function(fun = dnorm, geom = "point", n = 20)
+#' base + stat_function(fun = dnorm, n = 20)
 #'
-#' # Plot a normal curve
-#' ggplot(data.frame(x = c(-5, 5)), aes(x)) + stat_function(fun = dnorm)
+#' # Two functions on the same plot
+#' base +
+#'   stat_function(fun = dnorm, colour = "red") +
+#'   stat_function(fun = dt, colour = "blue", args = list(df = 1))
 #'
-#' # To specify a different mean or sd, use the args parameter to supply new values
-#' ggplot(data.frame(x = c(-5, 5)), aes(x)) +
-#'   stat_function(fun = dnorm, args = list(mean = 2, sd = .5))
+#' # Using a custom anonymous function
+#' base + stat_function(fun = function(.x) .5*exp(-abs(.x)))
+#' base + stat_function(fun = ~ .5*exp(-abs(.x)))
 #'
-#' # Two functions on the same plot
-#' f <- ggplot(data.frame(x = c(0, 10)), aes(x))
-#' f + stat_function(fun = sin, colour = "red") +
-#'   stat_function(fun = cos, colour = "blue")
+#' # Using a custom named function
+#' f <- function(.x) .5*exp(-abs(.x))
+#' base + stat_function(fun = f)
 #'
-#' # Using a custom function
-#' test <- function(x) {x ^ 2 + x + 20}
-#' f + stat_function(fun = test)
 stat_function <- function(mapping = NULL, data = NULL,
                           geom = "path", position = "identity",
                           ...,
@@ -97,6 +102,8 @@ StatFunction <- ggproto("StatFunction", Stat,
       x_trans <- scales$x$trans$inverse(xseq)
     }
 
+    if (is.formula(fun)) fun <- rlang::as_function(fun)
+
     new_data_frame(list(
       x = xseq,
       y = do.call(fun, c(list(quote(x_trans)), args))
diff --git a/man/stat_function.Rd b/man/stat_function.Rd
index 0a7fe4e0ff..096922e77e 100644
--- a/man/stat_function.Rd
+++ b/man/stat_function.Rd
@@ -39,13 +39,16 @@ often aesthetics, used to set an aesthetic to a fixed value, like
 \code{colour = "red"} or \code{size = 3}. They may also be parameters
 to the paired geom/stat.}
 
-\item{fun}{function to use. Must be vectorised.}
+\item{fun}{Function to use. Either 1) an anonymous function in the base or
+rlang formula syntax (see \code{\link[rlang:as_function]{rlang::as_function()}})
+or 2) a quoted or character name referencing a function; see examples. Must
+be vectorised.}
 
 \item{xlim}{Optionally, restrict the range of the function to this range.}
 
-\item{n}{number of points to interpolate along}
+\item{n}{Number of points to interpolate along}
 
-\item{args}{list of additional arguments to pass to \code{fun}}
+\item{args}{List of additional arguments to pass to \code{fun}}
 
 \item{na.rm}{If \code{FALSE}, the default, missing values are removed with
 a warning. If \code{TRUE}, missing values are silently removed.}
@@ -62,9 +65,9 @@ that define both data and aesthetics and shouldn't inherit behaviour from
 the default plot specification, e.g. \code{\link[=borders]{borders()}}.}
 }
 \description{
-This stat makes it easy to superimpose a function on top of an existing
-plot. The function is called with a grid of evenly spaced values along
-the x axis, and the results are drawn (by default) with a line.
+This stat makes it easy to superimpose a function on top of an existing plot.
+The function is called with a grid of evenly spaced values along the x axis,
+and the results are drawn (by default) with a line.
 }
 \section{Aesthetics}{
 
@@ -85,35 +88,39 @@ Learn more about setting these aesthetics in \code{vignette("ggplot2-specs")}.
 }
 
 \examples{
-set.seed(1492)
-df <- data.frame(
-  x = rnorm(100)
-)
-x <- df$x
-base <- ggplot(df, aes(x)) + geom_density()
-base + stat_function(fun = dnorm, colour = "red")
-base + stat_function(fun = dnorm, colour = "red", args = list(mean = 3))
-
-# Plot functions without data
-# Examples adapted from Kohske Takahashi
 
-# Specify range of x-axis
-ggplot(data.frame(x = c(0, 2)), aes(x)) +
-  stat_function(fun = exp, geom = "line")
+# stat_function is useful for overlaying functions
+set.seed(1492)
+ggplot(data.frame(x = rnorm(100)), aes(x)) +
+  geom_density() +
+  stat_function(fun = dnorm, colour = "red")
+
+# To plot functions without data, specify range of x-axis
+base <- ggplot(data.frame(x = c(-5, 5)), aes(x))
+base + stat_function(fun = dnorm)
+base + stat_function(fun = dnorm, args = list(mean = 2, sd = .5))
+
+# The underlying mechanics evaluate the function at discrete points
+# and connect the points with lines
+base <- ggplot(data.frame(x = c(-5, 5)), aes(x))
+base + stat_function(fun = dnorm, geom = "point")
+base + stat_function(fun = dnorm, geom = "point", n = 20)
+base + stat_function(fun = dnorm, n = 20)
 
-# Plot a normal curve
-ggplot(data.frame(x = c(-5, 5)), aes(x)) + stat_function(fun = dnorm)
+# Two functions on the same plot
+base +
+  stat_function(fun = dnorm, colour = "red") +
+  stat_function(fun = dt, colour = "blue", args = list(df = 1))
 
-# To specify a different mean or sd, use the args parameter to supply new values
-ggplot(data.frame(x = c(-5, 5)), aes(x)) +
-  stat_function(fun = dnorm, args = list(mean = 2, sd = .5))
+# Using a custom anonymous function
+base + stat_function(fun = function(.x) .5*exp(-abs(.x)))
+base + stat_function(fun = ~ .5*exp(-abs(.x)))
 
-# Two functions on the same plot
-f <- ggplot(data.frame(x = c(0, 10)), aes(x))
-f + stat_function(fun = sin, colour = "red") +
-  stat_function(fun = cos, colour = "blue")
+# Using a custom named function
+f <- function(.x) .5*exp(-abs(.x))
+base + stat_function(fun = f)
 
-# Using a custom function
-test <- function(x) {x ^ 2 + x + 20}
-f + stat_function(fun = test)
+}
+\seealso{
+\code{\link[rlang:as_function]{rlang::as_function()}}
 }
diff --git a/tests/testthat/test-stats-function.r b/tests/testthat/test-stats-function.r
index 6ef761718d..2444f4ef99 100644
--- a/tests/testthat/test-stats-function.r
+++ b/tests/testthat/test-stats-function.r
@@ -34,3 +34,16 @@ test_that("works with discrete x", {
   expect_equal(ret$x, 1:2)
   expect_equal(ret$y, 1:2)
 })
+
+test_that("works with formula syntax", {
+  dat <- data_frame(x = 1:10)
+
+  base <- ggplot(dat, aes(x, group = 1)) +
+    stat_function(fun = ~ .x^2, geom = "point", n = 5) +
+    scale_x_continuous(limits = c(0, 10))
+  ret <- layer_data(base)
+
+  s <- seq(0, 10, length.out = 5)
+  expect_equal(ret$x, s)
+  expect_equal(ret$y, s^2)
+})