It varies based on country and jurisdiction, but from an American / European perspective - some parts of the emulation scene are “definitely not legal” (eg, distributing copyrighted ROMs), and most parts of the scene are “It is complicated. Well-informed people have different predictions, but it hasn’t been tested in court, so we don’t know for sure”.

Moon Channel (an actual lawyer) has a fairly clear and concise summary with particular relation to the Dolphin emulator’s attempt to get itself on Steam: https://www.youtube.com/watch?v=wROQUZDCIMI