diff --git a/ci/travis/iwyu.sh b/ci/travis/iwyu.sh
index a3994fe80..85a797a89 100755
--- a/ci/travis/iwyu.sh
+++ b/ci/travis/iwyu.sh
@@ -3,6 +3,7 @@
 set -euo pipefail
 
 if [ "${OSTYPE-}" = msys ] && [ -z "${MINGW_DIR+x}" ]; then
+  # On Windows MINGW_DIR (analogous to /usr) might not always be defined when we need it for some tools
   if [ "${HOSTTYPE-}" = x86_64 ]; then
     MINGW_DIR=/mingw64
   elif [ "${HOSTTYPE-}" = i686 ]; then
@@ -12,27 +13,32 @@ fi
 invoke_cc() {
   local env_vars=() args=() env_parsed=0
   if [ "${OSTYPE}" = msys ]; then
+    # On Windows we don't want automatic path conversion, since it can break non-path arguments
     env_vars+=(MSYS2_ARG_CONV_EXCL="*")
   fi
   local arg; for arg in "$@"; do
     if [ 0 -ne "${env_parsed}" ]; then
+      # Nothing to do if we've already finished converting environment variables.
       args+=("${arg}")
     elif [ "${arg}" == "--" ]; then
+      # Reached '--'? Then we're finished parsing environment variables.
       env_parsed=1
     else
       if [ "${OSTYPE}" = msys ] && [ ! "${arg}" = "${arg#PATH=}" ]; then
-        local key="${arg%%=*}"
-        local value="${arg#*=}"
-        value="${value//'/'\\''}"
-        value="'${value//;/\' \'}'"
-        local paths; declare -a paths="(${value})"
+        # We need to split Windows-style paths and convert them to UNIX-style one-by-one.
+        local key="${arg%%=*}"  # name of environment variable
+        local value="${arg#*=}"  # value of environment variable
+        value="${value//'/'\\''}"  # Escape single quotes
+        value="'${value//;/\' \'}'"  # Replace semicolons by spaces for splitting
+        local paths; declare -a paths="(${value})"  # Split into array
         value=""
         local path; for path in "${paths[@]}"; do
           if [ "${OSTYPE}" = msys ]; then
-            path="${path//\\//}"
+            path="${path//\\//}"  # Convert 'C:\...' into 'C:/...'
           fi
           case "${path}" in
             [a-zA-Z]:|[a-zA-Z]:/*)
+              # Convert 'C:/...' into '/c/...'
               local drive; drive="${path%%:*}"
               path="/${drive,,}${path#*:}"
               ;;
@@ -41,9 +47,9 @@ invoke_cc() {
           if [ -n "${value}" ]; then
             value="${value}:"
           fi
-          value="${value}${path}"
+          value="${value}${path}"  # Replace with modified PATH
         done
-        arg="${key}=${value}"
+        arg="${key}=${value}"  # Replace the environment variable with the modified version
       fi
       env_vars+=("${arg}")
     fi
@@ -51,7 +57,9 @@ invoke_cc() {
   local cc; cc="${args[0]}"
   case "${cc##*/}" in
     clang*)
+      # Call iwyu with the modified arguments and environment variables (env -i starts with a blank slate)
       { PATH="${PATH}:/usr/bin" env -i "${env_vars[@]}" "${SHELL-/bin/bash}" -c 'iwyu -isystem "$("$1" -print-resource-dir "${@:2}")/include" "${@:2}"' exec "${args[@]}" 2>&1 || true; } | awk '
+        # Awk script to remove noise in the iwyu output
         { header = 0; }
         /^(The full include-list for .*|.* should (add|remove) these lines:)$/ { keep = 1; header = 1; }
         /^(The full include-list for ([^\/]*\/)*external\/.*|([^\/]*\/)*external\/.* should (add|remove) these lines:)$/ { keep = 0; header = 1; }
@@ -75,7 +83,8 @@ main() {
     data="$(exec tr "\n" "\a" <<< "${data}")"
     # Remove some fields that we don't want, and put back newlines we removed
     data="$(exec sed -e "s/\(0x[0-9a-fA-F]*\)]\(,\a\)/\"\1\"]\2/g" -e "s/,\(\a\s*\(]\|\$\)\)/\1/g" -e "s/\a/\n/g" <<< "${data}")"
-    # Parse the resulting JSON and select the actual fields we're interested in
+    # Parse the resulting JSON and select the actual fields we're interested in.
+    # We put the environment variables first, separating them from the command-line arguments via '--'.
     data="$(PATH="${PATH}:${MINGW_DIR-/usr}/bin" && exec jq -r '(
         []
         + [.[1:][] | select (.[0] == 6) | "\(.[1][1])=\(.[2][1])" | gsub("'\''"; "'\''\\'\'''\''") | "'\''\(.)'\''"]