I'll discuss various results on delta hyperbolic groups and locally CAT(-1) spaces. The emphasis will be on the conceptual ideas behind the proofs. Several open problems will also be posed. Some specific topics which will be touched upon (time permitting) include (1) rigidity (Mostow type & quasi-isometric) for certain singular locally CAT(-1) spaces, (2) pathologies in fixed point sets of involutions on boundaries at infinity of CAT(-1) manifolds, and (3) actions of hyperbolic groups on topological balls.