Abstract Theoretical models of the accumulation of Dobzhansky-Muller incompatibilities (DMIs) are studied, and in particular, the framework introduced by Orr (1995) and a verbal model introduced by Kondrashov et al. (2002). These models embody very different assumptions about the relationship between the substitution process underlying evolutionary divergence and the formation of incompatibilities. These differences have implications for our ability to make inferences about the divergence from patterns in the relevant data. With this in mind, the models are investigated for their ability to account for three patterns evident in this data: (1) the asymmetrical nature of incompatibilities under reciprocal introgression; (2) the finding that multiple concurrent introgressions may be necessary for an incompatibility to form; and (3) the finding that the probability of obtaining an incompatibility by introgressing a single amino acid remains roughly constant over a wide range of genetic distances. None of the models available in the literature can account for all of the empirical patterns. However, modified versions of the models can do so. Ways of discriminating between the different models are then discussed.