  Coalescing compact binaries are thought to be involved in a wide variety of
astrophysical phenomena. In particular, they are important sources of
gravitational radiation for both ground-based and space-based
laser-interferometer detectors, and they may be sources of supernova explosions
or gamma-ray bursts. Mergers of two white dwarfs may produce neutron stars with
peculiar properties, including perhaps millisecond radio pulsars sometimes
accompanied by planets (as observed in PSR 1257+12). According to a widely held
belief, the coalescence of two neutron stars should produce a rapidly rotating
black hole surrounded by an accretion disk or torus, but this is by no means
certain. This review paper focuses on the final hydrodynamic coalescence and
merger of double neutron stars and double white dwarfs, and addresses the
question of the nature of the final merger products.
