Bounded cohomology of acylindrically hyperbolic groups

Acylindrically hyperbolic groups form a vast collection of groups including non-elementary hyperbolic and relatively hyperbolic groups, mapping class groups, Out(F_n), many groups acting on CAT(0) cube complexes, and many others.
I will present a few results that describe their bounded cohomology in terms of their so-called hyperbolically embedded subgroups and, time permitting, discuss an expected connection with hyperbolic 3-manifolds.