Formal models of past human societies informed by archaeological research have a high potential for shaping some of the most topical current debates. Agent-based models, which emphasize how actions by individuals combine to produce global patterns, provide a convenient framework for developing quantitative models of historical social processes. However, being derived from computer science, the method remains largely specialized in archaeology. In this paper and the associated tutorial, we provide a jargon-free introduction to the technique, its potential and limits as well as its diverse applications in archaeology and beyond. We discuss the epistemological rationale of using computational modeling and simulation, classify types of models, and give an overview of the main concepts behind agent-based modeling.