The theory of relativity can be divided into two branches: the special and the general theory of relativity. Special relativity deals with fast moving objects, while General Relativity deals with the curving of time and space through massive objects like planets and stars (or more generally through any form of energy, remember: E=m c2), and the motion of objects in curved space-time. Superficially these two fields look very different, but Special Relativity can be considered as the limit of General Relativity when there is no curvature of space-time.
Special Relativity is now well understood and only little research is still done in this field. General Relativity is a very active research area; current research includes the physics of black holes and neutron stars, the study of how specific mass distributions exactly curve space-time, cosmology (the early universe), and the search for a theory of everything (quantum gravity, string theory).
Research on relativity at our Department is rather special: it turns out that light in a dielectric medium (like a prism or an optical fibre) propagates in the same way as it would in a curved space-time. This means that one can use optical experiments to test or illustrate effects in curved space-time. Conversely, one can use the mathematical apparatus of relativity (namely, differential geometry) to describe optical experiments in curved optical fibres, for instance.
Department members working on relativity: