Contractions of algebraic varieties are important in the study of their birational geometry via the minimal model program. Contraction algebras may be associated to certain such contractions, characterising how exceptional fibres deform, both classically and noncommutatively. I’ll survey joint work with Wemyss, and work of others including Bodzenta, Bondal, Hua, Kawamata, and Toda, in which these algebras are used to study the geometry of the contraction, investigate enumerative invariants, and construct symmetries of the derived category.