The domestication of plants and animals marks one of the most significant transitions in human, and indeed global, history. Traditionally, study of the domestication process was the exclusive domain of archaeologists and agricultural scientists; today it is an increasingly multidisciplinary enterprise that has come to involve the skills of evolutionary biologists and geneticists. Although the application of new information sources and methodologies has dramatically transformed our ability to study and understand domestication, it has also generated increasingly large and complex datasets, the interpretation of which is not straightforward. In particular, challenges of equifinality, evolutionary variance, and emergence of unexpected or counter-intuitive patterns all face researchers attempting to infer past processes directly from patterns in data. We argue that explicit modeling approaches, drawing upon emerging methodologies in statistics and population genetics, provide a powerful means of addressing these limitations. Modeling also offers an approach to analyzing datasets that avoids conclusions steered by implicit biases, and makes possible the formal integration of different data types. Here we outline some of the modeling approaches most relevant to current problems in domestication research, and demonstrate the ways in which simulation modeling is beginning to reshape our understanding of the domestication process.