Let G be a finite group, p a prime, B a Brauer p-block and k(B) the number of irreducible ordinary characters that belong to B.
Not a lot is known about the number k(B), besides a classical upper bound given by Richard Brauer and Walter Feit. However, a
lot has been conjectured. We report on the progress in some of the open problems on this invariant focusing on the classification
of defect groups of blocks with a fixed number k(B). This is joint work with Noelia Rizo and Lucia Sanus.