Under Islamic rule, which legal matters can kuffar regulate within their own community?

As far as I understand it, in an Islamic state, sharia generally applies to kuffar as well, but some legal matters are left to the kuffar to regulate within their community (I think marital and inheritance law fall in this category, but I'm not sure; some crimes may not apply either, such as apostasy, or zina, but those are guesses). Could we gather a comprehensive list of the legal matters that are left to kuffar communities to regulate for themselves?