diff --git a/NEWS.md b/NEWS.md
index a2282eee..2083fe06 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -8,6 +8,9 @@
   no longer think they are the right approach to solving this problem.
   See #768 for more information.
 
+* The `lift_*` family of functions has been deprecated. We no longer believe
+  these to be a good fit for purrr because rely on a style of function 
+  manipulation that is very uncommon in R code (#871).
 
 ## Features and fixes
 
diff --git a/R/composition.R b/R/composition.R
index 6ff3e6fb..0eb12e11 100644
--- a/R/composition.R
+++ b/R/composition.R
@@ -1,5 +1,8 @@
 #' Lift the domain of a function
 #'
+#' @description
+#' `r lifecycle::badge("deprecated")`
+#'
 #' `lift_xy()` is a composition helper. It helps you compose
 #' functions by lifting their domain from a kind of input to another
 #' kind. The domain can be changed from and to a list (l), a vector
@@ -12,6 +15,10 @@
 #' functional tools. Since this is such a common function,
 #' `lift()` is provided as an alias for that operation.
 #'
+#' We have deprecated these functions because we no longer believe "lifting"
+#' to be a mainstream operation, and we are striving to reduce purrr to its
+#' most useful core.
+#'
 #' @inheritParams as_vector
 #' @param ..f A function to lift.
 #' @param ... Default arguments for `..f`. These will be
@@ -41,36 +48,26 @@ NULL
 #'
 #' x <- list(x = c(1:100, NA, 1000), na.rm = TRUE, trim = 0.9)
 #' lift_dl(mean)(x)
-#'
-#' # Or in a pipe:
-#' mean %>% lift_dl() %>% invoke(x)
-#'
 #' # You can also use the lift() alias for this common operation:
 #' lift(mean)(x)
+#' # now:
+#' exec(mean, !!!x)
 #'
 #' # Default arguments can also be specified directly in lift_dl()
 #' list(c(1:100, NA, 1000)) %>% lift_dl(mean, na.rm = TRUE)()
+#' # now:
+#' mean(c(1:100, NA, 1000), na.rm = TRUE)
 #'
 #' # lift_dl() and lift_ld() are inverse of each other.
 #' # Here we transform sum() so that it takes a list
 #' fun <- sum %>% lift_dl()
 #' fun(list(3, NA, 4, na.rm = TRUE))
-#'
-#' # Now we transform it back to a variadic function
-#' fun2 <- fun %>% lift_ld()
-#' fun2(3, NA, 4, na.rm = TRUE)
-#'
-#' # It can sometimes be useful to make sure the lifted function's
-#' # signature has no named parameters, as would be the case for a
-#' # function taking only dots. The lifted function will take a list
-#' # or vector but will not match its arguments to the names of the
-#' # input. For instance, if you give a data frame as input to your
-#' # lifted function, the names of the columns are probably not
-#' # related to the function signature and should be discarded.
-#' lifted_identical <- lift_dl(identical, .unnamed = TRUE)
-#' mtcars[c(1, 1)] %>% lifted_identical()
-#' mtcars[c(1, 2)] %>% lifted_identical()
+#' # now:
+#' fun <- function(x) exec("sum", !!!x)
+#' exec(sum, 3, NA, 4, na.rm = TRUE)
 lift <- function(..f, ..., .unnamed = FALSE) {
+  lifecycle::deprecate_warn("0.4.0", "lift()")
+
   force(..f)
   defaults <- list(...)
   function(.x = list(), ...) {
@@ -88,6 +85,8 @@ lift_dl <- lift
 #' @rdname lift
 #' @export
 lift_dv <- function(..f, ..., .unnamed = FALSE) {
+  lifecycle::deprecate_warn("0.4.0", "lift_dv()")
+
   force(..f)
   defaults <- list(...)
 
@@ -111,21 +110,17 @@ lift_dv <- function(..f, ..., .unnamed = FALSE) {
 #'   type by supplying `.type`.
 #' @export
 #' @examples
-#' #
-#'
-#'
 #' ### Lifting from c(...) to list(...) or ...
 #'
 #' # In other situations we need the vector-valued function to take a
 #' # variable number of arguments as with pmap(). This is a job for
 #' # lift_vd():
-#' pmap(mtcars, lift_vd(mean))
-#'
-#' # lift_vd() will collect the arguments and concatenate them to a
-#' # vector before passing them to ..f. You can add a check to assert
-#' # the type of vector you expect:
-#' lift_vd(tolower, .type = character(1))("this", "is", "ok")
+#' pmap_dbl(mtcars, lift_vd(mean))
+#' # now
+#' pmap_dbl(mtcars, ~ mean(c(...)))
 lift_vl <- function(..f, ..., .type) {
+  lifecycle::deprecate_warn("0.4.0", "lift_vl()")
+
   force(..f)
   defaults <- list(...)
   if (missing(.type)) .type <- NULL
@@ -139,6 +134,8 @@ lift_vl <- function(..f, ..., .type) {
 #' @rdname lift
 #' @export
 lift_vd <- function(..f, ..., .type) {
+  lifecycle::deprecate_warn("0.4.0", "lift_vd()")
+
   force(..f)
   defaults <- list(...)
   if (missing(.type)) .type <- NULL
@@ -162,43 +159,20 @@ lift_vd <- function(..f, ..., .type) {
 #'
 #' @export
 #' @examples
-#' #
-#'
-#'
 #' ### Lifting from list(...) to c(...) or ...
 #'
-#' # cross() normally takes a list of elements and returns their
-#' # cartesian product. By lifting it you can supply the arguments as
-#' # if it was a function taking dots:
-#' cross_dots <- lift_ld(cross)
-#' out1 <- cross(list(a = 1:2, b = c("a", "b", "c")))
-#' out2 <- cross_dots(a = 1:2, b = c("a", "b", "c"))
-#' identical(out1, out2)
-#'
 #' # This kind of lifting is sometimes needed for function
 #' # composition. An example would be to use pmap() with a function
 #' # that takes a list. In the following, we use some() on each row of
 #' # a data frame to check they each contain at least one element
 #' # satisfying a condition:
-#' mtcars %>% pmap(lift_ld(some, partial(`<`, 200)))
-#'
-#' # Default arguments for ..f can be specified in the call to
-#' # lift_ld()
-#' lift_ld(cross, .filter = `==`)(1:3, 1:3) %>% str()
+#' mtcars %>% pmap_lgl(lift_ld(some, partial(`<`, 200)))
+#' # now
+#' mtcars %>% pmap_lgl(~ any(c(...) > 200))
 #'
-#'
-#' # Here is another function taking a list and that we can update to
-#' # take a vector:
-#' glue <- function(l) {
-#'   if (!is.list(l)) stop("not a list")
-#'   l %>% invoke(paste, .)
-#' }
-#'
-#' \dontrun{
-#' letters %>% glue()           # fails because glue() expects a list}
-#'
-#' letters %>% lift_lv(glue)()  # succeeds
 lift_ld <- function(..f, ...) {
+  lifecycle::deprecate_warn("0.4.0", "lift_ld()")
+
   force(..f)
   defaults <- list(...)
   function(...) {
@@ -209,6 +183,8 @@ lift_ld <- function(..f, ...) {
 #' @rdname lift
 #' @export
 lift_lv <- function(..f, ...) {
+  lifecycle::deprecate_warn("0.4.0", "lift_lv()")
+
   force(..f)
   defaults <- list(...)
   function(.x, ...) {
diff --git a/R/cross.R b/R/cross.R
index 9ce9e9a7..af21cccb 100644
--- a/R/cross.R
+++ b/R/cross.R
@@ -19,7 +19,7 @@
 #' )
 #'
 #' # With deprecated `cross()`
-#' data %>% cross() %>% map_chr(lift(paste))
+#' data %>% cross() %>% map_chr(~ paste(..., collapse = " "))
 #'
 #' # With `expand_grid()`
 #' tidyr::expand_grid(!!!data) %>% pmap_chr(paste)
diff --git a/_pkgdown.yml b/_pkgdown.yml
index 5d619523..422fed55 100644
--- a/_pkgdown.yml
+++ b/_pkgdown.yml
@@ -95,7 +95,6 @@ reference:
   contents:
   - faq-adverbs-export
   - compose
-  - lift
   - negate
   - partial
   - safely
diff --git a/man/cross.Rd b/man/cross.Rd
index a5e8dd34..87595a59 100644
--- a/man/cross.Rd
+++ b/man/cross.Rd
@@ -52,9 +52,10 @@ Here is an example of equivalent usages for \code{cross()} and
 )
 
 # With deprecated `cross()`
-data \%>\% cross() \%>\% map_chr(lift(paste))
-#> [1] "John! Hello."     "Jane! Hello."     "John! Bonjour."   "Jane! Bonjour."  
-#> [5] "John... Hello."   "Jane... Hello."   "John... Bonjour." "Jane... Bonjour."
+data \%>\% cross() \%>\% map_chr(~ paste(..., collapse = " "))
+#> [1] "John Hello. ! "     "Jane Hello. ! "     "John Bonjour. ! "  
+#> [4] "Jane Bonjour. ! "   "John Hello. ... "   "Jane Hello. ... "  
+#> [7] "John Bonjour. ... " "Jane Bonjour. ... "
 
 # With `expand_grid()`
 tidyr::expand_grid(!!!data) \%>\% pmap_chr(paste)
diff --git a/man/lift.Rd b/man/lift.Rd
index 99c0f9e0..0b10403d 100644
--- a/man/lift.Rd
+++ b/man/lift.Rd
@@ -44,18 +44,23 @@ input vectors. The latter can be any of the types returned by
 A function.
 }
 \description{
+\ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#deprecated}{\figure{lifecycle-deprecated.svg}{options: alt='[Deprecated]'}}}{\strong{[Deprecated]}}
+
 \code{lift_xy()} is a composition helper. It helps you compose
 functions by lifting their domain from a kind of input to another
 kind. The domain can be changed from and to a list (l), a vector
 (v) and dots (d). For example, \code{lift_ld(fun)} transforms a
 function taking a list to a function taking dots.
-}
-\details{
+
 The most important of those helpers is probably \code{lift_dl()}
 because it allows you to transform a regular function to one that
 takes a list. This is often essential for composition with purrr
 functional tools. Since this is such a common function,
 \code{lift()} is provided as an alias for that operation.
+
+We have deprecated these functions because we no longer believe "lifting"
+to be a mainstream operation, and we are striving to reduce purrr to its
+most useful core.
 }
 \section{from ... to \code{list(...)} or \code{c(...)}}{
 
@@ -97,85 +102,42 @@ with \code{.type}.
 
 x <- list(x = c(1:100, NA, 1000), na.rm = TRUE, trim = 0.9)
 lift_dl(mean)(x)
-
-# Or in a pipe:
-mean \%>\% lift_dl() \%>\% invoke(x)
-
 # You can also use the lift() alias for this common operation:
 lift(mean)(x)
+# now:
+exec(mean, !!!x)
 
 # Default arguments can also be specified directly in lift_dl()
 list(c(1:100, NA, 1000)) \%>\% lift_dl(mean, na.rm = TRUE)()
+# now:
+mean(c(1:100, NA, 1000), na.rm = TRUE)
 
 # lift_dl() and lift_ld() are inverse of each other.
 # Here we transform sum() so that it takes a list
 fun <- sum \%>\% lift_dl()
 fun(list(3, NA, 4, na.rm = TRUE))
-
-# Now we transform it back to a variadic function
-fun2 <- fun \%>\% lift_ld()
-fun2(3, NA, 4, na.rm = TRUE)
-
-# It can sometimes be useful to make sure the lifted function's
-# signature has no named parameters, as would be the case for a
-# function taking only dots. The lifted function will take a list
-# or vector but will not match its arguments to the names of the
-# input. For instance, if you give a data frame as input to your
-# lifted function, the names of the columns are probably not
-# related to the function signature and should be discarded.
-lifted_identical <- lift_dl(identical, .unnamed = TRUE)
-mtcars[c(1, 1)] \%>\% lifted_identical()
-mtcars[c(1, 2)] \%>\% lifted_identical()
-#
-
-
+# now:
+fun <- function(x) exec("sum", !!!x)
+exec(sum, 3, NA, 4, na.rm = TRUE)
 ### Lifting from c(...) to list(...) or ...
 
 # In other situations we need the vector-valued function to take a
 # variable number of arguments as with pmap(). This is a job for
 # lift_vd():
-pmap(mtcars, lift_vd(mean))
-
-# lift_vd() will collect the arguments and concatenate them to a
-# vector before passing them to ..f. You can add a check to assert
-# the type of vector you expect:
-lift_vd(tolower, .type = character(1))("this", "is", "ok")
-#
-
-
+pmap_dbl(mtcars, lift_vd(mean))
+# now
+pmap_dbl(mtcars, ~ mean(c(...)))
 ### Lifting from list(...) to c(...) or ...
 
-# cross() normally takes a list of elements and returns their
-# cartesian product. By lifting it you can supply the arguments as
-# if it was a function taking dots:
-cross_dots <- lift_ld(cross)
-out1 <- cross(list(a = 1:2, b = c("a", "b", "c")))
-out2 <- cross_dots(a = 1:2, b = c("a", "b", "c"))
-identical(out1, out2)
-
 # This kind of lifting is sometimes needed for function
 # composition. An example would be to use pmap() with a function
 # that takes a list. In the following, we use some() on each row of
 # a data frame to check they each contain at least one element
 # satisfying a condition:
-mtcars \%>\% pmap(lift_ld(some, partial(`<`, 200)))
-
-# Default arguments for ..f can be specified in the call to
-# lift_ld()
-lift_ld(cross, .filter = `==`)(1:3, 1:3) \%>\% str()
-
-
-# Here is another function taking a list and that we can update to
-# take a vector:
-glue <- function(l) {
-  if (!is.list(l)) stop("not a list")
-  l \%>\% invoke(paste, .)
-}
-
-\dontrun{
-letters \%>\% glue()           # fails because glue() expects a list}
+mtcars \%>\% pmap_lgl(lift_ld(some, partial(`<`, 200)))
+# now
+mtcars \%>\% pmap_lgl(~ any(c(...) > 200))
 
-letters \%>\% lift_lv(glue)()  # succeeds
 }
 \seealso{
 \code{\link[=invoke]{invoke()}}
diff --git a/tests/testthat/_snaps/composition.md b/tests/testthat/_snaps/composition.md
new file mode 100644
index 00000000..619bacaf
--- /dev/null
+++ b/tests/testthat/_snaps/composition.md
@@ -0,0 +1,33 @@
+# lift_* is deprecated
+
+    Code
+      . <- lift(mean)
+    Condition
+      Warning:
+      `lift()` was deprecated in purrr 0.4.0.
+    Code
+      . <- lift_dv(mean)
+    Condition
+      Warning:
+      `lift_dv()` was deprecated in purrr 0.4.0.
+    Code
+      . <- lift_vl(mean)
+    Condition
+      Warning:
+      `lift_vl()` was deprecated in purrr 0.4.0.
+    Code
+      . <- lift_vd(mean)
+    Condition
+      Warning:
+      `lift_vd()` was deprecated in purrr 0.4.0.
+    Code
+      . <- lift_ld(mean)
+    Condition
+      Warning:
+      `lift_ld()` was deprecated in purrr 0.4.0.
+    Code
+      . <- lift_lv(mean)
+    Condition
+      Warning:
+      `lift_lv()` was deprecated in purrr 0.4.0.
+
diff --git a/tests/testthat/test-composition.R b/tests/testthat/test-composition.R
index 57412bb9..b59cbd86 100644
--- a/tests/testthat/test-composition.R
+++ b/tests/testthat/test-composition.R
@@ -1,4 +1,17 @@
+test_that("lift_* is deprecated", {
+  expect_snapshot({
+    . <- lift(mean)
+    . <- lift_dv(mean)
+    . <- lift_vl(mean)
+    . <- lift_vd(mean)
+    . <- lift_ld(mean)
+    . <- lift_lv(mean)
+  })
+})
+
 test_that("lift_dl and lift_ld are inverses of each other", {
+  options(lifecycle_verbosity = "quiet")
+
   expect_identical(
     sum %>%
       lift_dl(.unnamed = TRUE) %>%
@@ -11,18 +24,22 @@ test_that("lift_dl and lift_ld are inverses of each other", {
 })
 
 test_that("lift_dv is from ... to c(...)", {
+  options(lifecycle_verbosity = "quiet")
   expect_equal(lift_dv(range, .unnamed = TRUE)(1:10), c(1, 10))
 })
 
 test_that("lift_vd is from c(...) to ...", {
+  options(lifecycle_verbosity = "quiet")
   expect_equal(lift_vd(mean)(1, 2), 1.5)
 })
 
 test_that("lift_vl is from c(...) to list(...)", {
+  options(lifecycle_verbosity = "quiet")
   expect_equal(lift_vl(mean)(list(1, 2)), 1.5)
 })
 
 test_that("lift_lv is from list(...) to c(...)", {
+  options(lifecycle_verbosity = "quiet")
   glue <- function(l) {
     if (!is.list(l)) stop("not a list")
     l %>% do.call(paste, .)