Particle Acceleration at Relativistic Shocks and Current Sheets

Simple kinematic theories of particle acceleration at relativistic shocks lead to the prediction of a high-energy spectral index of -1.1 for the energy flux of synchrotron photons. However, several effects can change this picture. In this paper I discuss this theory briefly and mention recent developments concerning shock formation and magnetic field generation. An additional mechanism must operate at lower energy and current sheets present a possible alternative acceleration site; I summarize some recent work on the relativistic version of these objects.