Gravitational waves - a prediction of Einstein's General Relativity - are among the most elusive signals incident on the Earth. These signals - ripples in the curvature of space-time - carry information about what is happening deep in the heart of some of the most violent events in the Universe. However their observation remains one of the most challenging problems in experimental astro-physics, as the measurement sensitivity required by the detectors is equivalent to measuring a change in the separation of the Earth and Sun by the diameter of an atom. A global network of such detectors - LIGO, Virgo and GEO - is now in operation, with enhanced versions being developed, and a space-borne detector, LISA, is planned as a joint ESA/NASA mission. In this talk, Professor Hough will discuss the nature of gravitational waves, their cosmological significance, how the detectors work, and the preliminary results which are already showing promise.