  We develop a comprehensive theoretical model of relativistic collisionless
pair shocks mediated by the current filamentation instability. We notably
characterize the noninertial frame in which this instability is of a mostly
magnetic nature, and describe at a microscopic level the deceleration and
heating of the incoming background plasma through its collisionless interaction
with the electromagnetic turbulence. Our model compares well to large-scale
2D3V PIC simulations, and provides an important touchstone for the
phenomenology of such plasma systems.
