diff --git a/r/NAMESPACE b/r/NAMESPACE
index 567353876ca..4cc8df46d33 100644
--- a/r/NAMESPACE
+++ b/r/NAMESPACE
@@ -22,7 +22,9 @@ S3method("names<-",ArrowTabular)
 S3method(Ops,ArrowDatum)
 S3method(Ops,Expression)
 S3method(Ops,array_expression)
+S3method(all,ArrowDatum)
 S3method(all,equal.ArrowObject)
+S3method(any,ArrowDatum)
 S3method(as.character,ArrowDatum)
 S3method(as.character,FileFormat)
 S3method(as.character,FragmentScanOptions)
diff --git a/r/R/compute.R b/r/R/compute.R
index 1b79d76f037..0641bf1615c 100644
--- a/r/R/compute.R
+++ b/r/R/compute.R
@@ -186,6 +186,35 @@ unique.ArrowDatum <- function(x, incomparables = FALSE, ...) {
   call_function("unique", x)
 }
 
+#' @export
+any.ArrowDatum <- function(..., na.rm = FALSE){
+  
+  a <- collect_arrays_from_dots(list(...))
+  result <- call_function("any", a)
+
+  if (!na.rm && a$null_count > 0 && !as.vector(result)) {
+    # Three-valued logic: with na.rm = FALSE, any(c(TRUE, NA)) returns TRUE but any(c(FALSE, NA)) returns NA
+    # TODO: C++ library should take na.rm for any/all (like ARROW-9054)
+    Scalar$create(NA)
+  } else {
+    result
+  }
+}
+
+#' @export
+all.ArrowDatum <- function(..., na.rm = FALSE){
+  
+  a <- collect_arrays_from_dots(list(...))
+  result <- call_function("all", a)
+  
+  if (!na.rm && a$null_count > 0 && as.vector(result)) {
+    # See comment above in any() about three-valued logic
+    Scalar$create(NA)
+  } else {
+    result
+  }
+}
+
 #' `match` and `%in%` for Arrow objects
 #'
 #' `base::match()` is not a generic, so we can't just define Arrow methods for
diff --git a/r/tests/testthat/test-compute-aggregate.R b/r/tests/testthat/test-compute-aggregate.R
index 77010579d78..0621b7779c7 100644
--- a/r/tests/testthat/test-compute-aggregate.R
+++ b/r/tests/testthat/test-compute-aggregate.R
@@ -351,3 +351,33 @@ test_that("value_counts", {
   expect_identical(as.data.frame(value_counts(a)), result_df)
   expect_identical(as.vector(value_counts(a)$counts), result_df$counts)
 })
+
+test_that("any.Array and any.ChunkedArray", {
+  
+  data <- c(1:10, NA, NA)
+
+  expect_vector_equal(any(input > 5), data)
+  expect_vector_equal(any(input < 1), data)
+  expect_vector_equal(any(input < 1, na.rm = TRUE), data)
+  
+  data_logical <- c(TRUE, FALSE, TRUE, NA, FALSE)
+  
+  expect_vector_equal(any(input), data_logical)
+  expect_vector_equal(any(input, na.rm = TRUE), data_logical)
+  
+})
+
+test_that("all.Array and all.ChunkedArray", {
+
+  data <- c(1:10, NA, NA)
+  
+  expect_vector_equal(all(input > 5), data)
+  expect_vector_equal(all(input < 11), data)
+  expect_vector_equal(all(input < 11, na.rm = TRUE), data)
+  
+  data_logical <- c(TRUE, TRUE, NA)
+  
+  expect_vector_equal(all(input), data_logical)
+  expect_vector_equal(all(input, na.rm = TRUE), data_logical)
+  
+})