Abstract: The detection of gravitational waves from astrophysical sources of gravitational waves is a realistic goal for the current generation of interferometric gravitational-wave detectors. Compact binary neutron stars or black holes which lose energy as gravitational waves and spiral together are among the most promising sources for ground-based gravitational wave detectors. The detection of the inspiral and mergers may bring bring a wealth of astronomical and astrophysical information. After reviewing the basic properties of these sources and current evidence in support of reasonable event rates, I will present the results of searches performed on LIGO data during the past two years. No gravitational waves have been detected as yet. The experience gained demonstrates our readiness to extract information about the sources; I will outline some of the fundamental issues that might be addressed with a direct observation of waves from these sources.