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Category theory originated, in part, as a technique for seeing a collection of similar results from disparate parts of mathematics as instances of a more general theory of mathematical structures and the relationships between structures. To encompass a wide range of results, it was necessary to develop a quite abstract collection of conditions that apply in many instances. As a result, mathematicians sometimes refer to category theory as ‘abstract nonsense’ — especially when they are taking advantage of its power of generality! Because of this generality, category theory has had a crucial influence of the study of the semantics of programming languages, often guiding or inspiring the discovery of the right concepts, definitions, structures, and theorems. As a tool for studying the semantics of programming languages, the usefulness of category theory goes beyond its position as a well-developed, general theory of mathematical structures. In many instances, the ‘categorical viewpoint’ matches much better with basic motivations in computer science than the alternative foundational theories.