Gravitational waves, ripples in the fabric of spacetime, were predicted by Einstein a year after he developed general relativity. However, they are so weak that they have not been directly detected to date. We only have indirect evidence of their existence. The LIGO obdervatory comprises three laser interferometers designed and built to measure gravitational waves directly for the first time. One of the best candidate sources of gravitational waves is the inspiral and collision of neutron stars and black holes. Dr. Stephen Fairhurst, a professor of physics at the University of Wisconsin-Milwaukee will describe current results and future prospects from searches for inspiralling binary systems with LIGO.