Artin groups are a generalization of braid groups, and arise as the fundamental groups of configuration spaces associated with Coxeter groups. A long-standing open problem, called the K(Π,1) conjecture, states that these configuration spaces are classifying spaces for the corresponding Artin groups. In the case of finite Coxeter groups, this was proved by Deligne in 1972. In the first part of this talk I will introduce Coxeter groups, Artin groups, and the K(Π,1) conjecture. Then I will outline a recent proof of the K(π,1) conjecture in the affine case and further developments in the hyperbolic case. This is joint work with Mario Salvetti and Emanuele Delucchi.