Quasiconvexity has been an integral part of the study of the coarse geometry of hyperbolic groups and spaces from the beginnings of geometric group theory. Inspired by this history, there has been much recent interest in generalizing various aspects of quasiconvexity to wider classes of groups and spaces. In this talk, I will discuss recent work joint with Davideo Spriano and Hung C Tran were we investigate quasiconvexity in the class of hierarchically hyperbolic spaces; a generalization of hyperbolic spaces which contains the mapping class group, right-angled Artin and Coxeter groups, and many 3-manifold groups. We show that quasiconvex subsets of hierarchically hyperbolic space exhibit many of the same properties of quasiconvex subsets of hyperbolic spaces and we can exploit these similarities to show that the hyperbolically embedded subgroups of hierarchically hyperbolic groups are exactly those which are almost malnormal and quasiconvex.