In this talk we will give a brief introduction to the theory of bicategories, in order to present a bicategorical gadget, called Mackey 2-functor, axiomatizing an ubiquitous phenomena in finite equivariant mathematics, especially in representation theory of finite groups and equivariant topology. The key point of this theory so far is the existence of a universal bicategory (the Mackey 2-motives) encoding the properties of such 2-functors, and allowing furthers constructions.