The notion of affine Deligne-Lusztig variety (ADLV) was first introduced by Rapoport, which has been applied to number theory such as the study of Shimura varieties and the realization of local Langlands correspondence. Many of such applications make use of the special cases where the ADLV admits a simple description. One large class of such cases is the ADLV of Coxeter type, which has been already classified by Görtz-He-Nie. However, many people (Chan-Ivanov, Howard-Fox-Imai, Trentin,...) have found examples which are not of Coxeter type but admit a simple description. In this talk, I will talk about recent progress on this kind of new examples, including my recent work for GLn.