Idioms, conceived as fixed multi-word expressions that conceptually encode non-compositional meaning, are linguistic units that raise a number of questions relevant in the study of language and mind (e.g., whether they are stored in the lexicon or in memory, whether they have internal or external syntax similar to other expressions of the language, whether their conventional use is parallel to their non-compositional meaning, whether they are processed in similar ways to regular compositional expressions of the language, etc.). Idioms show some similarities and differences with other sorts of formulaic expressions, the main types of idioms that have been characterized in the linguistic literature, and the dimensions on which idiomaticity lies. Syntactically, idioms manifest a set of syntactic properties, as well as a number of constraints that account for their internal and external structure. Semantically, idioms present an interesting behavior with respect to a set of semantic properties that account for their meaning (i.e., conventionality, compositionality, and transparency, as well as aspectuality, referentiality, thematic roles, etc.). The study of idioms has been approached from lexicographic and computational, as well as from psycholinguistic and neurolinguistic perspectives.