Formulaic sequences are strings of words jointly representing a meaning or function that is often, though not always, different from the literal meaning of the component words. There is evidence from clinical linguistics, psychology, and neurology that they are processed, stored, or accessed (or a combination of these) differently from other word strings that do not have the same “formulaic” properties. However, the extent of their presence in languages is unclear, and linguistic theories have different views about what they are, and how they sit in relation to words and grammar. Theorists also differ in whether they consider formulaic sequences to be learned whole and then gradually broken down (if necessary), or glued together from previously learned single words once it is noticed that the particular combination is frequent in the language. One persistent challenge for researchers is how to help second language learners master sufficient formulaic sequences to sound idiomatic.