There is a growing attention to magnetic reconnection in relativistic astrophysics, but basic mechanisms of relativistic reconnection have been poorly understood.  In this talk I will overview our numerical investigations on magnetic reconnection in relativistic pair plasmas.  Kinetic particle-in-cell (PIC) simulations demonstrate that reconnection is a powerful particle accelerator and that various kinetic instabilities take place.  Relativistic two-fluid and resistive relativistic magnetohydrodynamic (RRMHD) simulations show larger-scale pictures including various new shocks.  General features in these results as well as the relevance to the theoretical models will be presented.