  We present a short review of recent progress in studying QED effects of
interaction of ultra-relativistic laser pulses with vacuum and $e^-e^+$ plasma.
The development of laser technologies promises very rapid growth of laser
intensities in close future already. 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 of intensity $\sim 10^{26}$W/cm$^2$
or even higher. Therefore, discussion of nonlinear optical effects in vacuum
are becoming urgent for experimentalists and are currently gaining much
attention. We show that, in spite of the fact that the respective field
strength is still essentially less than $E_S=m^2c^3/e\hbar=1.32\cdot
10^{16}$V/cm, the nonlinear vacuum effects will be accessible for observation
at ELI and XCELS facilities. The most promissory for observation is the effect
of pair creation by laser pulse in vacuum. It is shown, that at intensities
$\sim 5\cdot 10^{25}$W/cm$^2$, creation even of a single pair is accompanied by
development of an avalanchelike QED cascade. There exists an important
distinctive feature of the laser-induced cascades, as compared with the air
showers arising due to primary cosmic ray 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). It is responsible also for acceleration of slow
particles. It is shown that the effect of pair creation imposes a natural limit
for attainable laser intensity. Apparently, the field strength $E\sim E_S$ is
not accessible for pair creating electromagnetic field at all.
