diff --git a/README.md b/README.md
index 1d32f85..4e9d6c5 100644
--- a/README.md
+++ b/README.md
@@ -527,10 +527,34 @@ Alternative to the `dirname` command.
 ```sh
 dirname() {
     # Usage: dirname "path"
-    dir=${1%%/}
+
+    # If '$1' is empty set 'dir' to '.', else '$1'.
+    dir=${1:-.}
+
+    # Strip all trailing forward-slashes '/' from
+    # the end of the string.
+    #
+    # "${dir##*[!/]}": Remove all non-forward-slashes
+    # from the start of the string, leaving us with only
+    # the trailing slashes.
+    # "${dir%%"${}"}:  Remove the result of the above
+    # substitution (a string of forward slashes) from the
+    # end of the original string.
+    dir=${dir%%"${dir##*[!/]}"}
+
+    # If the variable *does not* contain any forward slashes
+    # set its value to '.'.
     [ "${dir##*/*}" ] && dir=.
+
+    # Remove everything *after* the last forward-slash '/'.
     dir=${dir%/*}
 
+    # Again, strip all trailing forward-slashes '/' from
+    # the end of the string (see above).
+    dir=${dir%%"${dir##*[!/]}"}
+
+    # Print the resulting string and if it is empty,
+    # print '/'.
     printf '%s\n' "${dir:-/}"
 }
 ```
@@ -554,10 +578,27 @@ Alternative to the `basename` command.
 ```sh
 basename() {
     # Usage: basename "path" ["suffix"]
+
+    # Strip all trailing forward-slashes '/' from
+    # the end of the string.
+    #
+    # "${1##*[!/]}": Remove all non-forward-slashes
+    # from the start of the string, leaving us with only
+    # the trailing slashes.
+    # "${1%%"${}"}:  Remove the result of the above
+    # substitution (a string of forward slashes) from the
+    # end of the original string.
     dir=${1%${1##*[!/]}}
+
+    # Remove everything before the final forward-slash '/'.
     dir=${dir##*/}
+
+    # If a suffix was passed to the function, remove it from
+    # the end of the resulting string.
     dir=${dir%"$2"}
 
+    # Print the resulting string and if it is empty,
+    # print '/'.
     printf '%s\n' "${dir:-/}"
 }
 ```