Modularity is now generally recognized as a fundamental feature of organisms, one that may have profound consequences for evolution. Modularity has recently become a major focus of research in organismal biology across multiple disciplines including genetics, developmental biology, functional morphology, population and evolutionary biology. While the wealth of new data, and also new theory, has provided exciting and novel insights, the concept of modularity has become increasingly ambiguous. That ambiguity is underlain by diverse intuitions about what modularity means, and the ambiguity is not merely about the meaning of the word—the metrics of modularity are measuring different properties and the methods for delimiting modules delimit them by different, sometimes conflicting criteria. The many definitions, metrics and methods can lead to substantial confusion not just about what modularity means as a word but also about what it means for evolution. Here we review various concepts, using graphical depictions of modules. We then review some of the metrics and methods for analyzing modularity at different levels. To place these in theoretical context, we briefly review theories about the origins and evolutionary consequences of modularity. Finally, we show how mismatches between concepts, metrics and methods can produce theoretical confusion, and how potentially illogical interpretations can be made sensible by a better match between definitions, metrics, and methods.