Abstract: Affine Deligne-Lusztig varieties are a generalization of certain subvarieties of flag varieties that were used by Deligne and Lusztig in the 70s to realise representations of finite groups of Lie type. At the same time they play an important role to describe the geometry of the reduction modulo p of moduli spaces of abelian varieties. I will give an introduction to the topic and explain some recent geometric results.