  We review recent progress in understanding the hydrodynamics of compact
binary mergers using relativistic smoothed particle hydrodynamics (SPH) codes.
Recent results are discussed for both double neutron stars and black hole -
neutron star binaries. The gravitational wave signals from these mergers
contain a lot of information about the masses and radii of the stars and the
equation of state of the neutron star fluid. For black hole - neutron star
mergers, the final fate of the fluid and the gravitational wave emission depend
strongly on the mass ratio and the black hole spin.
