We present a short review of recent progress in studying QED effects within the interaction of ultra-relativistic laser pulses with vacuum and e - e + plasma. Current development in laser technologies promises very rapid growth of laser intensities in the near future. Two exawatt class facilities (ELI and XCELS, Russia) in Europe are already in the planning stage. Realization of these projects will make available a laser intensity of ∼ 1026 W/cm2 or even higher. Therefore, discussion of nonlinear optical effects in vacuum are becoming compelling for experimentalists and are currently gaining much attention. We show that, in spite of the fact that the expected field strength is still essentially less than E S = m 2 c 3/ eℏ = 1.32 · 1016 V/cm, the nonlinear vacuum effects will be accessible for observation at the ELI and XCELS facilities. The most promissory effect for observation is pair creation by a laser pulse in vacuum. It is shown, that at intensities ∼ 5 · 1025 W/cm2, creation even of a single pair is accompanied by the development of an avalanche QED cascade. There exists a distinctive feature of the laser-induced cascades, as compared with the air showers arising due primarily to cosmic rays entering the atmosphere. In our case the laser field plays not only the role of a target (similar to a nucleus in the case of air showers) but is also responsible for the acceleration of slow particles. It is shown that the effect of pair creation imposes a natural limit for the attainable laser intensity and, apparently, the field strength E ∼ E S is not accessible for a pair-creating electromagnetic field at all.