diff --git a/test/README.md b/test/README.md
index 5294a8e101f..ff9eda5ecaf 100644
--- a/test/README.md
+++ b/test/README.md
@@ -205,6 +205,10 @@ To run the YAML e2e tests, run the following command:
 
 ### Running upgrade tests
 
+There are two scenarios in upgrade tests. One is to install the previous release, upgrade to the current release, and
+validate whether the Tekton pipeline works. The other is to install the previous release, create the pipelines and tasks,
+upgrade to the current release, and validate whether the Tekton pipeline works.
+
 To run the upgrade tests, run the following command:
 
 ```bash
diff --git a/test/e2e-common.sh b/test/e2e-common.sh
index 0fca7b8ebca..af3e25fa237 100755
--- a/test/e2e-common.sh
+++ b/test/e2e-common.sh
@@ -135,7 +135,7 @@ function install_pipeline_crd() {
 # Install the Tekton pipeline crd based on the release number
 function install_pipeline_crd_version() {
   echo ">> Deploying Tekton Pipelines of Version $1"
-  kubectl apply -f "https://github.com/tektoncd/pipeline/releases/download/v$1/release.yaml" || fail_test "Build pipeline installation failed of Version $1"
+  kubectl apply -f "https://github.com/tektoncd/pipeline/releases/download/$1/release.yaml" || fail_test "Build pipeline installation failed of Version $1"
   verify_pipeline_installation
 }
 
@@ -161,7 +161,7 @@ function uninstall_pipeline_crd() {
 
 function uninstall_pipeline_crd_version() {
   echo ">> Uninstalling Tekton Pipelines of version $1"
-  kubectl delete --ignore-not-found=true -f "https://github.com/tektoncd/pipeline/releases/download/v$1/release.yaml"
+  kubectl delete --ignore-not-found=true -f "https://github.com/tektoncd/pipeline/releases/download/$1/release.yaml"
 
   # Make sure that everything is cleaned up in the current namespace.
   for res in conditions pipelineresources tasks pipelines taskruns pipelineruns; do
diff --git a/test/e2e-tests-upgrade.sh b/test/e2e-tests-upgrade.sh
index 4f8219cff90..56e9b320f2c 100755
--- a/test/e2e-tests-upgrade.sh
+++ b/test/e2e-tests-upgrade.sh
@@ -15,10 +15,17 @@
 # limitations under the License.
 
 # This script calls out to scripts in tektoncd/plumbing to setup a cluster
-# and deploy Tekton Pipelines to it for running integration tests.
+# and deploy Tekton Pipelines to it for running upgrading tests. There are
+# two scenarios we need to cover in this script:
+
+# Scenario 1: install the previous release, upgrade to the current release, and
+# validate whether the Tekton pipeline works.
+
+# Scenario 2: install the previous release, create the pipelines and tasks, upgrade
+# to the current release, and validate whether the Tekton pipeline works.
 
 source $(dirname $0)/e2e-common.sh
-PREVIOUS_PIPELINE_VERSION=0.5.2
+PREVIOUS_PIPELINE_VERSION=v0.5.2
 
 # Script entry point.
 
@@ -30,16 +37,20 @@ header "Setting up environment"
 set +o errexit
 set +o pipefail
 
+# First, we will verify if Scenario 1 works.
+# Install the previous release.
 header "Install the previous release of Tekton pipeline $PREVIOUS_PIPELINE_VERSION"
 install_pipeline_crd_version $PREVIOUS_PIPELINE_VERSION
 
+# Upgrade to the current release.
 header "Upgrade to the current release of Tekton pipeline"
 install_pipeline_crd
 
-# Run the tests
+# Run the integration tests.
 failed=0
 go_test_e2e -timeout=20m ./test || failed=1
 
+# Run the post-integration tests.
 for test in taskrun pipelinerun; do
   header "Running YAML e2e tests for ${test}s"
   if ! run_yaml_tests ${test}; then
@@ -50,23 +61,32 @@ for test in taskrun pipelinerun; do
   fi
 done
 
-# Remove all the pipeline CRDs
+# Remove all the pipeline CRDs, and clean up the environment for next Scenario.
 uninstall_pipeline_crd
 uninstall_pipeline_crd_version $PREVIOUS_PIPELINE_VERSION
 
+# Next, we will verify if Scenario 2 works.
+# Install the previous release.
 header "Install the previous release of Tekton pipeline $PREVIOUS_PIPELINE_VERSION"
 install_pipeline_crd_version $PREVIOUS_PIPELINE_VERSION
 
+# Create the resources of taskrun and pipelinerun, under the directories example/taskrun
+# and example/pipelinerun.
 for test in taskrun pipelinerun; do
   header "Applying the resources ${test}s"
   apply_resources ${test}
 done
 
+# Upgrade to the current release.
 header "Upgrade to the current release of Tekton pipeline"
 install_pipeline_crd
 
+# Run the integration tests.
 go_test_e2e -timeout=20m ./test || failed=1
 
+# Run the post-integration tests. We do not need to install the resources again, since
+# they are installed before the upgrade. We verify if they still work, after going through
+# the upgrade.
 for test in taskrun pipelinerun; do
   header "Running YAML e2e tests for ${test}s"
   if ! run_tests ${test}; then