Computational modelling allows researchers to combine the rich detail of qualitative research with the rigour of quantitative and formal research, as well as to represent complex structures and processes within a theoretical model. After an introduction to modelling, the authors discuss the role of computational methods in the social sciences. They treat computational methods, including dynamic simulation, knowledge-based models and machine learning, as a single broad class of research tools and develop a framework for incorporating them within established traditions of social science research. They provide a concise description of each method and a variety of social science illustrations, including four detailed examples.