Hyperbolic 3-manifold groups have many surjections to finite groups. The structure of the fundamental group as a subgroup of PSL(2,C) gives surjections to PSL(2,F) for many finite fields. But, by work of Lubotzky these quotients are sparse. To better understand surjections to other finite simple groups, I will discuss ongoing work on alternating quotients of twist knot groups. This is joint work with Chloe George and Neil Hoffman.