Randomness is a way to discuss generic or typical behavior of a group. In this talk, I will discuss random quotients of certain classes of groups. Quotients of hyperbolic groups (groups that act geometrically on a hyperbolic space) and their generalizations have long been a powerful tool for proving strong algebraic results. I will focus on random quotients of acylindrical and hierarchically hyperbolic groups (HHGs), two generalizations of hyperbolic groups that include mapping class groups, most CAT(0) cubical groups including right-angled Artin and Coxeter groups, many 3–manifold groups, and various combinations of such groups. In this context, I will explain why a random quotient of an HHG that does not split as a direct product is again an HHG, definitivelyshowing that the class of HHGs is quite broad. I will also describe how the result can also be applied to understand the geometry of random quotients of hyperbolic and relatively hyperbolic groups. This is joint work with Dan Berlyne, Giorgio Mangioni, Thomas Ng, and Alexander Rasmussen.