Abstract: While the basic study of cardinals are undeniably important in mathematics, they are surprisingly ill-behaved in the constructive setting, where they are currently poorly understood. In this seminar, I will present a series of novel constructive results on cardinals, including a constructivization of the Cantor-Schröder-Bernstein theorem,a predicative proof of the uncountability of the (MacNeille) reals, and, if time permits, a constructivization of König’s theorem. Along the way, I will highlight aspects and challenges in the study of constructive cardinals, as well as some ways to tackle them.