Grammatical Inference (GI) concentrates on finding compact representations, i.e. grammars, of possibly infinite sets of sentences. These grammars describe what sentences do or do not belong to a particular language. The process of learning the form of a grammar based on example sentences from the language touches several fields. Here, we give an overview of the field of GI as well as fields that are closely related. We discuss linguistic, empirical, and formal grammatical inference and discuss the work that falls in the areas where these fields overlap.