 In this article we introduce modern constructive mathematics based on the BHK-interpretation of the logical connectives and quantifiers. We discuss four major varieties of constructive mathematics, with particular emphasis on the two varieties associated with Errett Bishop and Per Martin-Löf, which can be regarded as minimal constructive systems. We then outline progress in (informal) constructive reverse mathematics, a research programme seeking to identify principles, such as Brouwer’s fan theorem, that, added to the minimal constructive varieties, facilitate proofs of important analytic theorems. After a brief discussion of constructive algebra, economics, and finance, the entry ends with two appendices: one on certain logical principles that hold in classical, intuitionistic, and recursive mathematics and which, added to Bishop’s constructive mathematics, facilitate the proof of certain useful theorems of analysis; and one discussing approaches to a constructive development of general topology. 