Abstract.  At present the ELI facility is planned in Europe. It is one of the goals of ELI to generate extreme external electromagnetic fields. From the theory of Quantum Electromagnetism in strong fields it is known that ultra-intense radiation is capable of destabilizing the quantum vacuum well below the Schwinger field in the presence of initial seeds. Seed particles could be electrons, positrons, or photons. The presence of super-strong external fields allow processes that are otherwise forbidden. Hence, it is expected that cascades of electrons, positrons, and photons can be generated that lead to large multiplicities of the original seeds under optimal conditions. In the talk the theoretical foundations of strong field QED are revisited. Next proper transport equations based on the QED effects are formulated. The latter are solved numerically. Comparison with analytical predictions is given.