æ is in purely Latin words like ex æquo, et cætera, or curriculum vitæ, that's all. œ appears in œil (eye) so you see that a lot more commonly already, but I can't think of any other word that uses it off the top of my head (beside other derivated words like œillères). (pardon the puns)

Wikipedia gives examples of "curriculum vitæ" and "et cætera." We use those both as loanwords in English, but I've only seen it as the separate letters "ae," not the ligature æ.

The Nordic languages use ö or ø instead, in Swedish also ä is used instead of æ.