Simultaneously modeling hybridization and the multispecies coalescent is becoming increasingly common, and inference of species networks in this context is now implemented in several software packages. This article addresses some of the conceptual issues and decisions to be made in this modeling, including whether or not to use branch lengths and issues with model identifiability. This article is based on a talk given at a Spotlight Session at Evolution 2017 meeting in Portland, Oregon. This session included several talks about modeling hybridization and gene flow in the presence of incomplete lineage sorting. Other talks given at this meeting are also included in this special issue of Systematic Biology.