Exactness is a weak version of amenability for discrete groups. It can be described in geometric, analytic or dynamical terms and has numerous applications. The most striking one was proved by Yu: exact groups satisfy the coarse Baum-Connes conjecture and consequently, the Novikov conjecture. For this reason exactness has recently become popular in areas such as geometric group theory, operator algebras or index theory.

In this talk we will give an introduction to the notion of exactness, discuss open questions and some of the recent results involving this class of groups.