The representation theory of finite groups was introduced at the end of the 1800s with the work of Frobenius and Schur. It was developed further through contributions by Brauer, Burnside, Green and others, and together with its applications, has become an important theory for itself.

On the other hand, beginning around the mid-20th century, category theory started to develop and, together with the abstraction techniques it provides, rapidly spread into other fields.

Parallel to the development of category theory, categorical representations (i.e., those representations within which the techniques of category theory are intensively used) become popular inside representation theory.

The aim of this talk is to describe the evolution of functorial representation theory and to discuss the theory of biset functors, one of the most effective techniques of this new style of representation theory, and to describe various applications of this technique.