Observers and theorists discuss the latest developments in the astrophysics of neutron stars, black holes and their interaction in the universe. Often found in compact, interacting binaries, these objects exhibit broadly similar behaviour. The determination of observational signatures that distinguish between these two types is explored. Supernovae and evolutionary scenarios leading to neutron stars and black holes, single or in binaries, are discussed in detail. There is also a discussion of the mystery of cosmic gamma ray bursts, currently thought to represent enormous stellar explosions at cosmological distances. These could be the result of mergers of a neutron star and its compact binary companion: a literal neutron star-black hole connection. This text provides a series of lectures for the advanced graduate student and presents material that should prove useful to the research astrophysicist and space physicist.