English has two verbs that are identical in the present tense, and close enough in meaning to cause trouble: hang/hanged/hanged and hang/hung/hung.

Ironically, in Lerner and Lowe’s great musical success, My Fair Lady, linguist and grammar purist Henry Higgins makes this very mistake in the opening lines of his first song, “Why Can’t the English Teach Their Children How to Speak?” He says, of Cockney Eliza Doolittle:
“By rights she should be taken out and hung
For the cold-blooded murder of the English tongue.”

The “hang” that uses “hanged” as its past tense and past participle means to execute someone on the gallows.

The “hang” that uses “hung” as its past tense and past participle means to suspend, as a picture on a wall.
So Henry Higgins should have said, “taken out and hanged.” But then, of course, the rhyme with “English tongue” would disappear. We’ll call it poetic license, perhaps.
In short, persons executed in the old-fashioned way were “hanged” and everything else that is suspended is “hung.”
Curiously, the word “hung” is also used in slang to refer to a sexually well-endowed male. This is the usage that makes the following joke possible: “Did you hear about the plastic surgeon who hung himself?” If you don’t know the difference between these two verbs, you would wonder what was supposed to be funny.