We will first take a brief tour of the Cohen--Lenstra heuristics and its generalizations. In particular, I'll talk about: how these heuristics are related to random matrices, how to use Hurwitz schemes to prove the function field case (Ellenberg--Venkatesh--Westerland), how to modify the heuristics when the base field contains roots of unity (Lipnowski--Tsimerman and Lipnowski--Tsimerman--Sawin), and how to construct the non-abelian generalization of the heuristics (Liu--Wood--Zureick-Brown). In the end, I'll discuss the modification of the non-abelian Cohen--Lenstra heuristics when the base field contains roots of unity, and the construction of a non-abelian random group model for this case. Speaker(s): Yuan Liu (University of Michigan)