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After invention of high-contrast petawatt-level lasers, a new class of fast and strongly non-stationary processes has been exposed for investigations. This new class is characterized by considerable charge separation arising from interaction of superintense laser pulses with nano-dimensional targets such as nanofilms, nanowires, and nanoclusters. Below, two important examples of such processes will be considered. The first one is formation of relativistic electron mirrors from nanofilms by accelerating laser pulses [1,2] and generation of coherent ultrashort x-ray pulses through Thomson backscattering of a probe laser pulse off such mirrors [3,4]. The second example considers generation of intense infrared and terahertz radiation during acceleration and relaxation of electrons expelled from nano-dimensional targets by a powerful laser pulse. An idea for synchronous acceleration of electrons from a nanofilm with a superintense nonadiabatic laser pulse was considered in [1,2]. For a nonadiabatic laser pulse of relativistic amplitude incident normally at the nanofilm, all electrons can be expelled simultaneously out of the nanofilm in the longitudinal direction (along the laser beam axis) due to the action of the longitudinal component of the Lorentz force. As a result, a relativistic electron mirror can be formed - an electron bunch with diameter of several micrometers and thickness of several nanometers or less. Accelerating laser pulse should be relativistic with amplitude exceeding some threshold, besides the front of the laser pulse should be sharp enough. Reflections of the counter-propagating probe laser pulses off relativistic electron mirrors were investigated numerically. In this case, parameters of x-ray pulse, such as amplitude, frequency, envelope, phase, etc., can be controlled easily [4]. When nanowires, nanoclusters, or mass-limited nanofilms are used as a target, expelled electron bunch can be very compact in space and its charge can be on a nanocoulomb-level. Radiated during acceleration electromagnetic pulse can contain from a half-cycle to several cycles of oscillations and its frequency can belong to the terahertz or infrared bands. It is shown that the amplitude of radiation can be on relativistic level for modern petawatt laser systems.