Abstract: The existence of a population of compact neutron star binaries serves as a unique probe of general relativity and of binary stellar evolution. Mergers of neutron star binaries are promising sources for the detection of gravitational radiation. Yet, to inspiral and merge in less than a Hubble time, a compact binary must be separated by less than the radii of its main sequence progenitors. To reach their current small separations, these binaries must have passed through a common envelope phase. Reconciling the observed distribution of neutron star masses in binaries with theories of accretion during common envelope has posed a long-standing problem. This talk explores the hydrodynamics of common envelope with the goal of reconciling theories for the formation of neutron stars in close binaries with the narrow observed distribution of neutron star masses.<br>