diff --git a/NEWS.md b/NEWS.md
index 61683895da..32327bbcfd 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -21,6 +21,9 @@
 
 * ggplot2 now works in Turkish locale (@yutannihilation, #3011).
 
+* `coord_sf()`, `coord_map()`, and `coord_polar()` now squash `-Inf` and `Inf`
+  into the min and max of the plot (@yutannihilation, #2972).
+
 # ggplot2 3.1.0
 
 ## Breaking changes
diff --git a/R/coord-map.r b/R/coord-map.r
index fa507198b5..d1f1448472 100644
--- a/R/coord-map.r
+++ b/R/coord-map.r
@@ -116,6 +116,10 @@ CoordMap <- ggproto("CoordMap", Coord,
 
     out$x <- rescale(out$x, 0:1, panel_params$x.proj)
     out$y <- rescale(out$y, 0:1, panel_params$y.proj)
+    # mproject() converts Inf to NA, so we need to restore them from data.
+    out$x[is.infinite(data$x)] <- squish_infinite(data$x)
+    out$y[is.infinite(data$y)] <- squish_infinite(data$y)
+
     out
   },
 
diff --git a/R/coord-polar.r b/R/coord-polar.r
index 0169990750..c7d61d02c3 100644
--- a/R/coord-polar.r
+++ b/R/coord-polar.r
@@ -337,10 +337,12 @@ theta_rescale_no_clip <- function(coord, x, panel_params) {
 }
 
 theta_rescale <- function(coord, x, panel_params) {
+  x <- squish_infinite(x, panel_params$theta.range)
   rotate <- function(x) (x + coord$start) %% (2 * pi) * coord$direction
   rotate(rescale(x, c(0, 2 * pi), panel_params$theta.range))
 }
 
 r_rescale <- function(coord, x, panel_params) {
+  x <- squish_infinite(x, panel_params$r.range)
   rescale(x, c(0, 0.4), panel_params$r.range)
 }
diff --git a/R/sf.R b/R/sf.R
index 4d54e4c459..f59b8c396a 100644
--- a/R/sf.R
+++ b/R/sf.R
@@ -433,7 +433,7 @@ CoordSf <- ggproto("CoordSf", CoordCartesian,
       function(x) sf_rescale01_x(x, panel_params$y_range)
     )
 
-    data
+    transform_position(data, squish_infinite, squish_infinite)
   },
 
 
diff --git a/tests/testthat/test-coord-map.R b/tests/testthat/test-coord-map.R
index 3976a22551..39a3493b04 100644
--- a/tests/testthat/test-coord-map.R
+++ b/tests/testthat/test-coord-map.R
@@ -11,3 +11,15 @@ test_that("USA state map drawn", {
       coord_map("mercator")
   )
 })
+
+test_that("Inf is squished to range", {
+  d <- cdata(
+    ggplot(data_frame(x = 0, y = 0)) +
+      geom_point(aes(x,y)) +
+      annotate("text", -Inf, Inf, label = "Top-left") +
+      coord_map()
+  )
+
+  expect_equal(d[[2]]$x, 0)
+  expect_equal(d[[2]]$y, 1)
+})
diff --git a/tests/testthat/test-coord-polar.r b/tests/testthat/test-coord-polar.r
index 4e6057a0f5..f0b92fe166 100644
--- a/tests/testthat/test-coord-polar.r
+++ b/tests/testthat/test-coord-polar.r
@@ -65,6 +65,22 @@ test_that("clipping can be turned off and on", {
   expect_equal(coord$clip, "off")
 })
 
+test_that("Inf is squished to range", {
+  d <- cdata(
+    ggplot(data_frame(x = "a", y = 1), aes(x, y)) +
+      geom_col() +
+      coord_polar() +
+      annotate("text", Inf, Inf, label = "Top-Center") +
+      annotate("text", -Inf, -Inf, label = "Center-Center")
+  )
+
+  # 0.4 is the upper limit of radius hardcoded in r_rescale()
+  expect_equal(d[[2]]$r, 0.4)
+  expect_equal(d[[2]]$theta, 0)
+  expect_equal(d[[3]]$r, 0)
+  expect_equal(d[[3]]$theta, 0)
+})
+
 
 # Visual tests ------------------------------------------------------------
 
diff --git a/tests/testthat/test-coord_sf.R b/tests/testthat/test-coord_sf.R
index 4db7937a9f..baf56d6dbc 100644
--- a/tests/testthat/test-coord_sf.R
+++ b/tests/testthat/test-coord_sf.R
@@ -160,3 +160,15 @@ test_that("axis labels can be set manually", {
 
 })
 
+test_that("Inf is squished to range", {
+  skip_if_not_installed("sf")
+
+  d <- cdata(
+    ggplot(sf::st_point(c(0, 0))) +
+      geom_sf() +
+      annotate("text", -Inf, Inf, label = "Top-left")
+  )
+
+  expect_equal(d[[2]]$x, 0)
+  expect_equal(d[[2]]$y, 1)
+})