Under which circumstances is sympatric speciation possible? An answer to this long-standing question of evolutionary biology has turned out to be challenging. In particular, models for the evolution of assortative mating under frequency-dependent disruptive selection necessarily depend on a large number of ecological and genetic factors. For this reason, most previous approaches to this issue depend on individual-based simulations. However, simulation studies with only slightly different assumptions have come to wildly different conclusions, making it hard to generalize results and leading to fierce debate.