diff --git a/r/DESCRIPTION b/r/DESCRIPTION
index ffc473f365d..4678d0a236b 100644
--- a/r/DESCRIPTION
+++ b/r/DESCRIPTION
@@ -60,6 +60,7 @@ Collate:
     'chunked-array.R'
     'io.R'
     'compression.R'
+    'scalar.R'
     'compute.R'
     'config.R'
     'csv.R'
@@ -85,7 +86,6 @@ Collate:
     'record-batch-writer.R'
     'reexports-bit64.R'
     'reexports-tidyselect.R'
-    'scalar.R'
     'schema.R'
     'struct.R'
     'util.R'
diff --git a/r/NAMESPACE b/r/NAMESPACE
index 6a8c0f9b3ea..01604ab0a9b 100644
--- a/r/NAMESPACE
+++ b/r/NAMESPACE
@@ -15,8 +15,17 @@ S3method(Ops,ChunkedArray)
 S3method(Ops,Expression)
 S3method(Ops,array_expression)
 S3method(all,equal.ArrowObject)
+S3method(as.character,Array)
+S3method(as.character,ChunkedArray)
+S3method(as.character,Scalar)
 S3method(as.data.frame,RecordBatch)
 S3method(as.data.frame,Table)
+S3method(as.double,Array)
+S3method(as.double,ChunkedArray)
+S3method(as.double,Scalar)
+S3method(as.integer,Array)
+S3method(as.integer,ChunkedArray)
+S3method(as.integer,Scalar)
 S3method(as.list,RecordBatch)
 S3method(as.list,Table)
 S3method(as.raw,Buffer)
@@ -44,6 +53,9 @@ S3method(length,Array)
 S3method(length,ChunkedArray)
 S3method(length,Scalar)
 S3method(length,Schema)
+S3method(mean,Array)
+S3method(mean,ChunkedArray)
+S3method(mean,Scalar)
 S3method(names,Dataset)
 S3method(names,RecordBatch)
 S3method(names,ScannerBuilder)
@@ -58,6 +70,9 @@ S3method(read_message,MessageReader)
 S3method(read_message,default)
 S3method(row.names,RecordBatch)
 S3method(row.names,Table)
+S3method(sum,Array)
+S3method(sum,ChunkedArray)
+S3method(sum,Scalar)
 S3method(tail,Array)
 S3method(tail,ChunkedArray)
 S3method(tail,RecordBatch)
diff --git a/r/R/array.R b/r/R/array.R
index f17ea56cb01..194cdeb42f8 100644
--- a/r/R/array.R
+++ b/r/R/array.R
@@ -341,3 +341,12 @@ is.Array <- function(x, type = NULL) {
   }
   is_it
 }
+
+#' @export
+as.double.Array <- function(x, ...) as.double(as.vector(x), ...)
+
+#' @export
+as.integer.Array <- function(x, ...) as.integer(as.vector(x), ...)
+
+#' @export
+as.character.Array <- function(x, ...) as.character(as.vector(x), ...)
diff --git a/r/R/chunked-array.R b/r/R/chunked-array.R
index f3a3eaec9fb..5a8df533c8a 100644
--- a/r/R/chunked-array.R
+++ b/r/R/chunked-array.R
@@ -75,8 +75,6 @@ ChunkedArray <- R6Class("ChunkedArray", inherit = ArrowObject,
       if (is.integer(i)) {
         i <- Array$create(i)
       }
-      # Invalid: Tried executing function with non-value type: ChunkedArray
-      # so use old methods
       shared_ptr(ChunkedArray, call_function("take", self, i))
     },
     Filter = function(i, keep_na = TRUE) {
@@ -151,3 +149,12 @@ head.ChunkedArray <- head.Array
 
 #' @export
 tail.ChunkedArray <- tail.Array
+
+#' @export
+as.double.ChunkedArray <- as.double.Array
+
+#' @export
+as.integer.ChunkedArray <- as.integer.Array
+
+#' @export
+as.character.ChunkedArray <- as.character.Array
diff --git a/r/R/compute.R b/r/R/compute.R
index 000c5c86f07..a860b0ef91f 100644
--- a/r/R/compute.R
+++ b/r/R/compute.R
@@ -16,12 +16,73 @@
 # under the License.
 
 #' @include array.R
+#' @include chunked-array.R
+#' @include scalar.R
 
 call_function <- function(function_name, ..., options = list()) {
   assert_that(is.string(function_name))
   compute__CallFunction(function_name, list(...), options)
 }
 
+#' @export
+sum.Array <- function(..., na.rm = FALSE) scalar_aggregate("sum", ..., na.rm = na.rm)
+
+#' @export
+sum.ChunkedArray <- sum.Array
+
+#' @export
+sum.Scalar <- sum.Array
+
+#' @export
+mean.Array <- function(..., na.rm = FALSE) scalar_aggregate("mean", ..., na.rm = na.rm)
+
+#' @export
+mean.ChunkedArray <- mean.Array
+
+#' @export
+mean.Scalar <- mean.Array
+
+min.Array <- function(..., na.rm = FALSE) {
+  extrema <- scalar_aggregate("minmax", ..., na.rm = na.rm)
+  # TODO: StructScalar needs field accessor methods in C++: ARROW-9070
+  Scalar$create(as.vector(extrema)$min)
+}
+
+scalar_aggregate <- function(FUN, ..., na.rm = FALSE) {
+  a <- collect_arrays_from_dots(list(...))
+  if (!na.rm && a$null_count > 0) {
+    # Arrow sum/mean function always drops NAs so handle that here
+    # https://issues.apache.org/jira/browse/ARROW-9054
+    Scalar$create(NA_integer_, type = a$type)
+  } else {
+    if (inherits(a$type, "Boolean")) {
+      # Bool sum/mean not implemented so cast to int
+      # https://issues.apache.org/jira/browse/ARROW-9055
+      a <- a$cast(int8())
+    }
+    shared_ptr(Scalar, call_function(FUN, a))
+  }
+}
+
+collect_arrays_from_dots <- function(dots) {
+  # Given a list that may contain both Arrays and ChunkedArrays,
+  # return a single ChunkedArray containing all of those chunks
+  # (may return a regular Array if there is only one element in dots)
+  assert_that(all(map_lgl(dots, is.Array)))
+  if (length(dots) == 1) {
+    return(dots[[1]])
+  }
+
+  arrays <- unlist(lapply(dots, function(x) {
+    if (inherits(x, "ChunkedArray")) {
+      x$chunks
+    } else {
+      x
+    }
+  }))
+  ChunkedArray$create(!!!arrays)
+}
+
 CastOptions <- R6Class("CastOptions", inherit = ArrowObject)
 
 #' Cast options
@@ -32,12 +93,10 @@ CastOptions <- R6Class("CastOptions", inherit = ArrowObject)
 #' @param allow_float_truncate allow float truncate, `!safe` by default
 #'
 #' @export
-cast_options <- function(
-  safe = TRUE,
-  allow_int_overflow = !safe,
-  allow_time_truncate = !safe,
-  allow_float_truncate = !safe
-){
+cast_options <- function(safe = TRUE,
+                         allow_int_overflow = !safe,
+                         allow_time_truncate = !safe,
+                         allow_float_truncate = !safe) {
   shared_ptr(CastOptions,
     compute___CastOptions__initialize(allow_int_overflow, allow_time_truncate, allow_float_truncate)
   )
diff --git a/r/R/record-batch.R b/r/R/record-batch.R
index 78d28cf3cb4..2ecde6fb285 100644
--- a/r/R/record-batch.R
+++ b/r/R/record-batch.R
@@ -119,8 +119,6 @@ RecordBatch <- R6Class("RecordBatch", inherit = ArrowObject,
         i <- Array$create(i)
       }
       assert_is(i, "Array")
-      # Invalid: Tried executing function with non-value type: RecordBatch
-      # so use old methods
       shared_ptr(RecordBatch, call_function("take", self, i))
     },
     Filter = function(i, keep_na = TRUE) {
diff --git a/r/R/scalar.R b/r/R/scalar.R
index df06f7b3a38..f824c2ed8f6 100644
--- a/r/R/scalar.R
+++ b/r/R/scalar.R
@@ -38,6 +38,7 @@ Scalar <- R6Class("Scalar", inherit = ArrowObject,
   ),
   active = list(
     is_valid = function() Scalar__is_valid(self),
+    null_count = function() sum(!self$is_valid),
     type = function() DataType$create(Scalar__type(self))
   )
 )
@@ -62,3 +63,12 @@ is.na.Scalar <- function(x) !x$is_valid
 
 #' @export
 as.vector.Scalar <- function(x, mode) x$as_vector()
+
+#' @export
+as.double.Scalar <- as.double.Array
+
+#' @export
+as.integer.Scalar <- as.integer.Array
+
+#' @export
+as.character.Scalar <- as.character.Array
diff --git a/r/R/table.R b/r/R/table.R
index 785a10979c6..73a25e76315 100644
--- a/r/R/table.R
+++ b/r/R/table.R
@@ -146,8 +146,6 @@ Table <- R6Class("Table", inherit = ArrowObject,
       if (is.integer(i)) {
         i <- Array$create(i)
       }
-      # Invalid: Tried executing function with non-value type: Table
-      # so use old methods
       shared_ptr(Table, call_function("take", self, i))
     },
     Filter = function(i, keep_na = TRUE) {
diff --git a/r/src/compute.cpp b/r/src/compute.cpp
index b83576d3d26..11ac2aeda69 100644
--- a/r/src/compute.cpp
+++ b/r/src/compute.cpp
@@ -160,6 +160,12 @@ std::shared_ptr<arrow::compute::FunctionOptions> make_compute_options(
     return out;
   }
 
+  if (func_name == "minmax") {
+    auto out = std::make_shared<arrow::compute::MinMaxOptions>(
+        arrow::compute::MinMaxOptions::Defaults());
+    return out;
+  }
+
   return nullptr;
 }
 
diff --git a/r/tests/testthat/test-compute.R b/r/tests/testthat/test-compute.R
index 1d0d23a788d..4c2d0f26bd4 100644
--- a/r/tests/testthat/test-compute.R
+++ b/r/tests/testthat/test-compute.R
@@ -17,6 +17,102 @@
 
 context("compute")
 
+test_that("sum.Array", {
+  ints <- 1:5
+  a <- Array$create(ints)
+  expect_is(sum(a), "Scalar")
+  expect_identical(as.integer(sum(a)), sum(ints))
+
+  floats <- c(1.3, 2.4, 3)
+  f <- Array$create(floats)
+  expect_identical(as.numeric(sum(f)), sum(floats))
+
+  floats <- c(floats, NA)
+  na <- Array$create(floats)
+  expect_identical(as.numeric(sum(na)), sum(floats))
+  expect_is(sum(na, na.rm = TRUE), "Scalar")
+  expect_identical(as.numeric(sum(na, na.rm = TRUE)), sum(floats, na.rm = TRUE))
+
+  bools <- c(TRUE, TRUE, FALSE)
+  b <- Array$create(bools)
+  expect_identical(as.integer(sum(b)), sum(bools))
+})
+
+test_that("sum.ChunkedArray", {
+  a <- ChunkedArray$create(1:4, c(1:4, NA), 1:5)
+  expect_is(sum(a), "Scalar")
+  expect_true(is.na(as.vector(sum(a))))
+  expect_identical(as.numeric(sum(a, na.rm = TRUE)), 35)
+})
+
+test_that("sum dots", {
+  a1 <- Array$create(1:4)
+  a2 <- ChunkedArray$create(1:4, c(1:4, NA), 1:5)
+  expect_identical(as.numeric(sum(a1, a2, na.rm = TRUE)), 45)
+})
+
+test_that("sum.Scalar", {
+  skip("No sum method in arrow for Scalar: ARROW-9056")
+  s <- Scalar$create(4)
+  expect_identical(as.numeric(s), as.numeric(sum(s)))
+})
+
+test_that("mean.Array", {
+  ints <- 1:4
+  a <- Array$create(ints)
+  expect_is(mean(a), "Scalar")
+  expect_identical(as.vector(mean(a)), mean(ints))
+
+  floats <- c(1.3, 2.4, 3)
+  f <- Array$create(floats)
+  expect_identical(as.vector(mean(f)), mean(floats))
+
+  floats <- c(floats, NA)
+  na <- Array$create(floats)
+  expect_identical(as.vector(mean(na)), mean(floats))
+  expect_is(mean(na, na.rm = TRUE), "Scalar")
+  expect_identical(as.vector(mean(na, na.rm = TRUE)), mean(floats, na.rm = TRUE))
+
+  bools <- c(TRUE, TRUE, FALSE)
+  b <- Array$create(bools)
+  expect_identical(as.vector(mean(b)), mean(bools))
+})
+
+test_that("mean.ChunkedArray", {
+  a <- ChunkedArray$create(1:4, c(1:4, NA), 1:5)
+  expect_is(mean(a), "Scalar")
+  expect_true(is.na(as.vector(mean(a))))
+  expect_identical(as.vector(mean(a, na.rm = TRUE)), 35/13)
+})
+
+test_that("mean.Scalar", {
+  skip("No mean method in arrow for Scalar: ARROW-9056")
+  s <- Scalar$create(4)
+  expect_identical(as.vector(s), mean(s))
+})
+
 test_that("Bad input handling of call_function", {
   expect_error(call_function("sum", 2, 3), "to_datum: Not implemented for type double")
 })
+
+test_that("min/max.Array", {
+  skip("arrow::MakeArrayFromScalar can't handle struct: ARROW-6604")
+  ints <- 1:4
+  a <- Array$create(ints)
+  expect_is(min(a), "Scalar")
+  expect_identical(as.vector(min(a)), min(ints))
+
+  floats <- c(1.3, 3, 2.4)
+  f <- Array$create(floats)
+  expect_identical(as.vector(min(f)), min(floats))
+
+  floats <- c(floats, NA)
+  na <- Array$create(floats)
+  expect_identical(as.vector(min(na)), min(floats))
+  expect_is(min(na, na.rm = TRUE), "Scalar")
+  expect_identical(as.vector(min(na, na.rm = TRUE)), min(floats, na.rm = TRUE))
+
+  bools <- c(TRUE, TRUE, FALSE)
+  b <- Array$create(bools)
+  expect_identical(as.vector(min(b)), min(bools))
+})