This thesis presents several important aspects of the plasma dynamics in extremely high intensity electromagnetic fields when quantum electrodynamics effects have to be taken into account. This work is of utmost importance for the forthcoming generation of multipetawatt laser facilities where this physics will be tested. The first part consists of an introduction that extends from classical and quantum electrodynamics in strong fields to the kinetic description of plasmas in the interaction with such fields. This can be considered as an advanced tutorial which would be extremely...