Laser-generated plasma gratings are dynamic optical elements for the manipulation of coherent light at high intensities, beyond the damage threshold of solid-stated based materials. Their formation, evolution and final collapse require a detailed understanding. In this paper, we present a model to explain the nonlinear dynamics of high amplitude plasma gratings in the spatially periodic ponderomotive potential generated by two identical counter-propagating lasers. Both, fluid and kinetic aspects of the grating dynamics are analyzed. It is shown that the adiabatic electron compression plays a crucial role as the electron pressure may reflect the ions from the grating and induce the grating to break in an X-type manner. A single parameter is found to determine the behaviour of the grating and distinguish three fundamentally different regimes for the ion dynamics: completely reflecting, partially reflecting/partially passing, and crossing. Criteria for saturation and life-time of the grating as well as the effect of finite ion temperature are presented.