The mod p points of a Shimura variety have a conjectural description called the Langlands-Rapoport conjecture. In accordance with the conjecture, Rapoport defined (generalized) affine Deligne-Lusztig varieties as the (conjectural) p-part of the description, in his Astérisque paper. Since then, various authors have studied their basic geometric properties including nonemptiness, dimensions, and connected components. Depending on what variants of affine Deligne-Lusztig varieties one studies, such questions are completely solved or moderately open. In this talk, I would like to explain what is known, what is conjectured, or what is completely open without any conjectures on the questions of basic geometric properties aforementioned, introducing my recent works among which is jointly with Ian Gleason and Yujie Xu.
