Explore the concept of hyperbolically embedded subgroups within acylindrically hyperbolic groups in this 53-minute lecture from the Workshop on Geometry of Subgroups. Delve into definitions, examples, and geometric properties of these special subgroups. Examine connections to random walks, action extensions, quasicocycle extensions, and relative hyperbolicity. Discover how virtually cyclic hyperbolically embedded subgroups serve as powerful tools for proving key results about acylindrically hyperbolic groups. Gain insights into the application of these subgroups in mathematical proofs, with no prior knowledge of the topic required.