diff --git a/r/R/dplyr-functions.R b/r/R/dplyr-functions.R
index 808956efe15..e9d0d17f730 100644
--- a/r/R/dplyr-functions.R
+++ b/r/R/dplyr-functions.R
@@ -839,7 +839,6 @@ agg_funcs$var <- function(x, na.rm = FALSE, ddof = 1) {
     options = list(skip_nulls = na.rm, min_count = 0L, ddof = ddof)
   )
 }
-
 agg_funcs$n_distinct <- function(x, na.rm = FALSE) {
   list(
     fun = "count_distinct",
@@ -847,7 +846,6 @@ agg_funcs$n_distinct <- function(x, na.rm = FALSE) {
     options = list(na.rm = na.rm)
   )
 }
-
 agg_funcs$n <- function() {
   list(
     fun = "sum",
@@ -855,6 +853,28 @@ agg_funcs$n <- function() {
     options = list()
   )
 }
+agg_funcs$min <- function(..., na.rm = FALSE) {
+  args <- list2(...)
+  if (length(args) > 1) {
+    arrow_not_supported("Multiple arguments to min()")
+  }
+  list(
+    fun = "min",
+    data = args[[1]],
+    options = list(skip_nulls = na.rm, min_count = 0L)
+  )
+}
+agg_funcs$max <- function(..., na.rm = FALSE) {
+  args <- list2(...)
+  if (length(args) > 1) {
+    arrow_not_supported("Multiple arguments to max()")
+  }
+  list(
+    fun = "max",
+    data = args[[1]],
+    options = list(skip_nulls = na.rm, min_count = 0L)
+  )
+}
 
 output_type <- function(fun, input_type) {
   # These are quick and dirty heuristics.
diff --git a/r/src/compute.cpp b/r/src/compute.cpp
index c6ba0a28046..a01c35be4ef 100644
--- a/r/src/compute.cpp
+++ b/r/src/compute.cpp
@@ -171,10 +171,11 @@ std::shared_ptr<arrow::compute::FunctionOptions> make_compute_options(
     return out;
   }
 
-  if (func_name == "min_max" || func_name == "sum" || func_name == "mean" ||
-      func_name == "any" || func_name == "all" || func_name == "hash_min_max" ||
-      func_name == "hash_sum" || func_name == "hash_mean" || func_name == "hash_any" ||
-      func_name == "hash_all") {
+  if (func_name == "all" || func_name == "hash_all" || func_name == "any" ||
+      func_name == "hash_any" || func_name == "mean" || func_name == "hash_mean" ||
+      func_name == "min_max" || func_name == "hash_min_max" || func_name == "min" ||
+      func_name == "hash_min" || func_name == "max" || func_name == "hash_max" ||
+      func_name == "sum" || func_name == "hash_sum") {
     using Options = arrow::compute::ScalarAggregateOptions;
     auto out = std::make_shared<Options>(Options::Defaults());
     if (!Rf_isNull(options["min_count"])) {
diff --git a/r/tests/testthat/test-dataset.R b/r/tests/testthat/test-dataset.R
index 14157545d61..837bf8048c5 100644
--- a/r/tests/testthat/test-dataset.R
+++ b/r/tests/testthat/test-dataset.R
@@ -621,17 +621,15 @@ test_that("Creating UnionDataset", {
 })
 
 test_that("map_batches", {
+  skip("map_batches() is broken (ARROW-14029)")
   skip_if_not_available("parquet")
   ds <- open_dataset(dataset_dir, partitioning = "part")
-  expect_warning(
-    expect_equivalent(
-      ds %>%
-        filter(int > 5) %>%
-        select(int, lgl) %>%
-        map_batches(~ summarize(., min_int = min(int))),
-      tibble(min_int = c(6L, 101L))
-    ),
-    "pulling data into R" # ARROW-13502
+  expect_equivalent(
+    ds %>%
+      filter(int > 5) %>%
+      select(int, lgl) %>%
+      map_batches(~ summarize(., min_int = min(int))),
+    tibble(min_int = c(6L, 101L))
   )
 })
 
diff --git a/r/tests/testthat/test-dplyr-group-by.R b/r/tests/testthat/test-dplyr-group-by.R
index 18be2a9304a..d6abb20c01c 100644
--- a/r/tests/testthat/test-dplyr-group-by.R
+++ b/r/tests/testthat/test-dplyr-group-by.R
@@ -28,9 +28,8 @@ test_that("group_by groupings are recorded", {
       group_by(chr) %>%
       select(int, chr) %>%
       filter(int > 5) %>%
-      summarize(min_int = min(int)),
-    tbl,
-    warning = TRUE
+      collect(),
+    tbl
   )
 })
 
@@ -62,9 +61,23 @@ test_that("ungroup", {
       select(int, chr) %>%
       ungroup() %>%
       filter(int > 5) %>%
-      summarize(min_int = min(int)),
-    tbl,
-    warning = TRUE
+      collect(),
+    tbl
+  )
+
+  # to confirm that the above expectation is actually testing what we think it's
+  # testing, verify that expect_dplyr_equal() distinguishes between grouped and
+  # ungrouped tibbles
+  expect_error(
+    expect_dplyr_equal(
+      input %>%
+        group_by(chr) %>%
+        select(int, chr) %>%
+        (function(x) if (inherits(x, "tbl_df")) ungroup(x) else x) %>%
+        filter(int > 5) %>%
+        collect(),
+      tbl
+    )
   )
 })
 
diff --git a/r/tests/testthat/test-dplyr-summarize.R b/r/tests/testthat/test-dplyr-summarize.R
index 12bb50fb3d5..c74ed6aa938 100644
--- a/r/tests/testthat/test-dplyr-summarize.R
+++ b/r/tests/testthat/test-dplyr-summarize.R
@@ -30,28 +30,6 @@ tbl$verses <- verses[[1]]
 tbl$padded_strings <- stringr::str_pad(letters[1:10], width = 2 * (1:10) + 1, side = "both")
 tbl$some_grouping <- rep(c(1, 2), 5)
 
-test_that("summarize", {
-  expect_dplyr_equal(
-    input %>%
-      select(int, chr) %>%
-      filter(int > 5) %>%
-      summarize(min_int = min(int)) %>%
-      collect(),
-    tbl,
-    warning = TRUE
-  )
-
-  expect_dplyr_equal(
-    input %>%
-      select(int, chr) %>%
-      filter(int > 5) %>%
-      summarize(min_int = min(int) / 2) %>%
-      collect(),
-    tbl,
-    warning = TRUE
-  )
-})
-
 test_that("summarize() doesn't evaluate eagerly", {
   expect_s3_class(
     Table$create(tbl) %>%
@@ -251,6 +229,131 @@ test_that("Group by n_distinct() on dataset", {
   )
 })
 
+test_that("summarize() with min() and max()", {
+  expect_dplyr_equal(
+    input %>%
+      select(int, chr) %>%
+      filter(int > 5) %>% # this filters out the NAs in `int`
+      summarize(min_int = min(int), max_int = max(int)) %>%
+      collect(),
+    tbl,
+  )
+  expect_dplyr_equal(
+    input %>%
+      select(int, chr) %>%
+      filter(int > 5) %>% # this filters out the NAs in `int`
+      summarize(
+        min_int = min(int + 4) / 2,
+        max_int = 3 / max(42 - int)
+      ) %>%
+      collect(),
+    tbl,
+  )
+  expect_dplyr_equal(
+    input %>%
+      select(int, chr) %>%
+      summarize(min_int = min(int), max_int = max(int)) %>%
+      collect(),
+    tbl,
+  )
+  expect_dplyr_equal(
+    input %>%
+      select(int) %>%
+      summarize(
+        min_int = min(int, na.rm = TRUE),
+        max_int = max(int, na.rm = TRUE)
+      ) %>%
+      collect(),
+    tbl,
+  )
+  expect_dplyr_equal(
+    input %>%
+      select(dbl, int) %>%
+      summarize(
+        min_int = -min(log(ceiling(dbl)), na.rm = TRUE),
+        max_int = log(max(as.double(int), na.rm = TRUE))
+      ) %>%
+      collect(),
+    tbl,
+  )
+
+  # multiple dots arguments to min(), max() not supported
+  expect_dplyr_equal(
+    input %>%
+      summarize(min_mult = min(dbl, int)) %>%
+      collect(),
+    tbl,
+    warning = "Multiple arguments to min\\(\\) not supported by Arrow"
+  )
+  expect_dplyr_equal(
+    input %>%
+      select(int, dbl, dbl2) %>%
+      summarize(max_mult = max(int, dbl, dbl2)) %>%
+      collect(),
+    tbl,
+    warning = "Multiple arguments to max\\(\\) not supported by Arrow"
+  )
+
+  # min(logical) or max(logical) yields integer in R
+  # min(Boolean) or max(Boolean) yields Boolean in Arrow
+  expect_dplyr_equal(
+    input %>%
+      select(lgl) %>%
+      summarize(
+        max_lgl = as.logical(max(lgl, na.rm = TRUE)),
+        min_lgl = as.logical(min(lgl, na.rm = TRUE))
+      ) %>%
+      collect(),
+    tbl,
+  )
+})
+
+test_that("min() and max() on character strings", {
+  expect_dplyr_equal(
+    input %>%
+      summarize(
+        min_chr = min(chr, na.rm = TRUE),
+        max_chr = max(chr, na.rm = TRUE)
+      ) %>%
+      collect(),
+    tbl,
+  )
+  skip("Strings not supported by hash_min_max (ARROW-13988)")
+  expect_dplyr_equal(
+    input %>%
+      group_by(fct) %>%
+      summarize(
+        min_chr = min(chr, na.rm = TRUE),
+        max_chr = max(chr, na.rm = TRUE)
+      ) %>%
+      collect(),
+    tbl,
+  )
+})
+
+test_that("summarise() with !!sym()", {
+  test_chr_col <- "int"
+  test_dbl_col <- "dbl"
+  test_lgl_col <- "lgl"
+  expect_dplyr_equal(
+    input %>%
+      group_by(false) %>%
+      summarise(
+        sum = sum(!!sym(test_dbl_col)),
+        any = any(!!sym(test_lgl_col)),
+        all = all(!!sym(test_lgl_col)),
+        mean = mean(!!sym(test_dbl_col)),
+        sd = sd(!!sym(test_dbl_col)),
+        var = var(!!sym(test_dbl_col)),
+        n_distinct = n_distinct(!!sym(test_chr_col)),
+        min = min(!!sym(test_dbl_col)),
+        max = max(!!sym(test_dbl_col))
+      ) %>%
+      collect(),
+    tbl
+  )
+})
+
 test_that("Filter and aggregate", {
   expect_dplyr_equal(
     input %>%