Nature has provided us with a fascinating laboratory for fundamental physics: binary neutron stars.  Very soon, these objects may be among the first to be detected by gravitational-wave laser interferometers which are currently under construction.  Such a detection would be a spectacular confirmation of Einstein’s theory of gravitation and would open a new observational window on strong-field gravitational processes.  I will review some important properties of neutron stars and general relativity, and will then discuss a new approach to modelling the adiabatic inspiral of neutron star binaries and their gravitational-wave emission.  These models can be used to construct wave templates, which will ultimately be needed to identify and interpret the signals from gravitational-wave detectors.