I have been able to find 4 options for put tile in place:
Thinset. Traditional use. Can be tricky on walls and ceilings. I've used it.
Mastic. Comes in two flavours: High VOC no longer sold in the US, and mostly water based. Older stuff tolerates some moisture. Newer stuff tends to become goop when wet. Ok for kitchen back splashes, not ok for showers or floors. I've used this laying vinyl floor tiles on concrete.
Epoxy. Multi component that you mix as needed. Difficult to work with.
Bondura. Essentially double sided sticky tape. Because it's so thin, there is zero tolerance for surface protrusions.
Is there a category I've missed?
E.g. lime and gypsum mixes that harden through carbonate formation from air, but still have creep ability and crack healing ability.