Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Constructive reverse mathematics is reverse mathematics carried out in Bishop-style constructive math (BISH)---that is, using intuitionistic logic and, where necessary, constructive ZF set theory. There are two primary foci of constructive reverse mathematics:

* first, investigating which constructive principles are necessary to prove a given constructive theorem; * secondly, investigating what non-constructive principles are necessary additions to BISH in order to prove a given non-constructive theorem.

I will introduce basic ideas of constructive mathematics and constructive reverse mathematics, paying particular attention to connections between various continuity properties, versions of the fan theorem, and a simple principle due to Ishihara.