The basic rules for hyphenation deal with hyphenating compound modifiers, not just compounds. A compound modifier is two or more words working like an adjective to modify another word, usually a noun.

On-air challenge: I'm going to give you three words, one of which is an animal. You give me a fourth word that can follow each of mine to complete a compound word or a familiar two-word phrase ...

One remarkable feature of compound words is that they don’t translate well at all from one language to another, at least when it comes to translating their constituent parts literally.