Affine Deligne-Lusztig varieties are a generalization of a class of varieties that was used in the 70s by Deligne and Lusztig to study representations of finite groups of Lie type. They play an important role to describe the geometry of a class of moduli spaces that is central in the Langlands program in arithmetic geometry. In my talk I will give an introduction and motivation of some of the main questions on affine Deligne-Lusztig varieties. Then I will propose a strategy towards solving these questions, and explain first recent successes.