Automated theorem proving is the use of computers to prove or disprove mathematical or logical statements. Such statements can express properties of hardware or software systems, or facts about the world that are relevant for applications such as natural language processing and planning. A brief introduction to propositional and first‐order logic is given, along with some of the main methods of automated theorem proving in these logics. These methods of theorem proving include resolution, Davis and Putnam‐style approaches, and others. Methods for handling the equality axioms are also presented. Methods of theorem proving in propositional logic are presented first, and then methods for first‐order logic. WIREs Cogn Sci 2014, 5:115–128. doi: 10.1002/wcs.1269This article is categorized under: Computer Science > Artificial Intelligence Philosophy > Artificial Intelligence Philosophy > Knowledge and Belief