Please excuse me if I bring up LOST in this post.
Mythology is a pretty big part of human culture, whether we notice it often or not. Think about Egypt and Greece for a moment. And Norse mythology too. There is stuff we see every day that relates to it. There are weird creatures and interesting people and useful lessons in the mythology of all cultures that we encounter in reading (A Portrait of the Artist as a Young Man, and many, many others) and in movies (Inception had a lot in there) and in television shows (cough, cough, LOST; I could go on and on about this one) and maybe we have even used it in our own writing.
This is a broad topic, and there are many things to discuss here, so why don't we just have a little comment chat, you know, if anybody actually reads my humble blog. So whether it's naming characters and giving them traits that correspond with it or it's using mythology to reveal your theme, what is it that you do in your own writing, no matter what the culture?