  The goal of this article is to survey some recent developments in the study
of groups acting on hyperbolic spaces. We focus on the class of acylindrically
hyperbolic groups; it is broad enough to include many examples of interest, yet
a significant part of the theory of hyperbolic and relatively hyperbolic groups
can be generalized in this context. In particular, we discuss group theoretic
Dehn filling and small cancellation theory in acylindrically hyperbolic groups.
Many results discussed here rely on the new generalization of relative
hyperbolicity based on the notion of a hyperbolically embedded subgroup.
