diff --git a/README.md b/README.md
index bc061aee..d5fdb3a0 100644
--- a/README.md
+++ b/README.md
@@ -106,3 +106,37 @@ Kubernetes releases:
 
     CSI_PROW_KUBERNETES_VERSION=1.13.3 ./.prow.sh
     CSI_PROW_KUBERNETES_VERSION=latest ./.prow.sh
+
+Dependencies and vendoring
+--------------------------
+
+Most projects will (eventually) use `go mod` to manage
+dependencies. `dep` is also still supported by `csi-release-tools`,
+but not documented here because it's not recommended anymore.
+
+The usual instructions for using [go
+modules](https://github.com/golang/go/wiki/Modules) apply. Here's a cheat sheet
+for some of the relevant commands:
+- list available updates: `GO111MODULE=on go list -u -m all`
+- update or add a single dependency: `GO111MODULE=on go get <package>`
+- update all dependencies to their next minor or patch release:
+  `GO111MODULE=on go get ./...` (add `-u=patch` to limit to patch
+  releases)
+- lock onto a specific version: `GO111MODULE=on go get <package>@<version>`
+- clean up `go.mod`: `GO111MODULE=on go mod tidy`
+- update vendor directory: `GO111MODULE=on go mod vendor`
+
+`GO111MODULE=on` can be left out when using Go >= 1.13 or when the
+source is checked out outside of `$GOPATH`.
+
+`go mod tidy` must be used to ensure that the listed dependencies are
+really still needed. Changing import statements or a tentative `go
+get` can result in stale dependencies.
+
+The `test-vendor` verifies that it was used when run locally or in a
+pre-merge CI job. If a `vendor` directory is present, it will also
+verify that it's content is up-to-date.
+
+The `vendor` directory is optional. It is still present in projects
+because it avoids downloading sources during CI builds. If this is no
+longer deemed necessary, then a project can also remove the directory.
diff --git a/build.make b/build.make
index 142c8578..c8384c16 100644
--- a/build.make
+++ b/build.make
@@ -125,6 +125,26 @@ test-fmt:
 # - the fabricated merge commit leaves go.mod, go.sum and vendor dir unchanged
 # - release-tools also didn't change (changing rules or Go version might lead to
 #   a different result and thus must be tested)
+# - import statements not changed (because if they change, go.mod might have to be updated)
+#
+# "git diff" is intelligent enough to annotate changes inside the "import" block in
+# the start of the diff hunk:
+#
+# diff --git a/rpc/common.go b/rpc/common.go
+# index bb4a5c4..5fa4271 100644
+# --- a/rpc/common.go
+# +++ b/rpc/common.go
+# @@ -21,7 +21,6 @@ import (
+#         "fmt"
+#         "time"
+#
+# -       "google.golang.org/grpc"
+#         "google.golang.org/grpc/codes"
+#         "google.golang.org/grpc/status"
+#
+# We rely on that to find such changes.
+#
+# Vendoring is optional when using go.mod.
 .PHONY: test-vendor
 test: test-vendor
 test-vendor:
@@ -135,22 +155,37 @@ test-vendor:
 			*v0.[56789]*) dep check && echo "vendor up-to-date" || false;; \
 			*) echo "skipping check, dep >= 0.5 required";; \
 		esac; \
-	  else \
-		echo "Repo uses 'go mod' for vendoring."; \
+	elif [ -f go.mod ]; then \
+		echo "Repo uses 'go mod'."; \
 		if [ "$${JOB_NAME}" ] && \
                    ( [ "$${JOB_TYPE}" != "presubmit" ] || \
-                     [ $$(git diff "${PULL_BASE_SHA}..HEAD" -- go.mod go.sum vendor release-tools | wc -l) -eq 0 ] ); then \
-			echo "Skipping vendor check because the Prow pre-submit job does not change vendoring."; \
-		elif ! GO111MODULE=on go mod vendor; then \
+                     [ $$( (git diff "${PULL_BASE_SHA}..HEAD" -- go.mod go.sum vendor release-tools; \
+                            git diff "${PULL_BASE_SHA}..HEAD" | grep -e '^@@.*@@ import (' -e '^[+-]import') | \
+		          wc -l) -eq 0 ] ); then \
+			echo "Skipping vendor check because the Prow pre-submit job does not affect dependencies."; \
+		elif ! GO111MODULE=on go mod tidy; then \
 			echo "ERROR: vendor check failed."; \
 			false; \
-		elif [ $$(git status --porcelain -- vendor | wc -l) -gt 0 ]; then \
-			echo "ERROR: vendor directory *not* up-to-date, it did get modified by 'GO111MODULE=on go mod vendor':"; \
-			git status -- vendor; \
-			git diff -- vendor; \
+		elif [ $$(git status --porcelain -- go.mod go.sum | wc -l) -gt 0 ]; then \
+			echo "ERROR: go module files *not* up-to-date, they did get modified by 'GO111MODULE=on go mod tidy':"; \
+			git diff -- go.mod go.sum; \
 			false; \
+		elif [ -d vendor ]; then \
+			if ! GO111MODULE=on go mod vendor; then \
+				echo "ERROR: vendor check failed."; \
+				false; \
+			elif [ $$(git status --porcelain -- vendor | wc -l) -gt 0 ]; then \
+				echo "ERROR: vendor directory *not* up-to-date, it did get modified by 'GO111MODULE=on go mod vendor':"; \
+				git status -- vendor; \
+				git diff -- vendor; \
+				false; \
+			else \
+				echo "Go dependencies and vendor directory up-to-date."; \
+			fi; \
+		else \
+			echo "Go dependencies up-to-date."; \
 		fi; \
-	 fi;
+	fi
 
 .PHONY: test-subtree
 test: test-subtree