The foremost 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 of objects is systematically explored. Supernovae and evolutionary scenarios leading to neutron stars and black holes, single or in binaries, are also discussed in detail. There is also a discussion of the decades old 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. A lucid series of lectures for the advanced graduate student. A unifying text that will appeal to the research astrophysicist and space physicist.