Supernova, gamma-ray bursts and other violent cosmic phenomenaare known (or believed) to drive strong, relativistic or sub-relativistic shocks. Unlike the standard hydrodynamic shocks mediated by particle-particle collisions, these shocks are collisionless and, hence, involve more complicated electromagnetic processes. Despite this, we often continue to use the hydrodynamic models to compare with observations. In this talk we will discuss important theoretical ideas developed recently in this field, and the role of the Weibel instability, in particular. We will then link them to the observational aspects, e.g., the radiation processes, the physics jitter radiation, and the effects relativistic kinematics on the observed spectra.