The interaction of ultra-intense (and ultra-short) laser beams with plasmas gives rise to a variety of phenomena. The propagation is, in principle, possible in an overdense plasma if the laser intensity is above a threshold fixed by the electron density. However, the solutions describing this so-called relativistically self-induced transparency are subject to violent electron instabilities, as is already the case in an underdense plasma. The growth rates of the instabilities are so large that it appears hopeless to propagate efficiently a high-intensity beam in a cold plasma. The situation is somewhat more favourable in a relativistically hot plasma, where the growth rates of the instabilities are significantly reduced. In any case, the interaction of the laser beam with the plasma results in a strong electron acceleration and heating. The electron acceleration is both due to the plasma waves generated in the plasma by the laser beam and to the laser field itself. In present-day experiments, the fastest electron energy can be in the range of hundreds of MeV. Correlatively, fast ions can be accelerated by the charge separation electric fields, and energetic photons due to bremsstrahlung appear, which in turn can be responsible for photonuclear reactions. The transport and interactions of all these energetic particles in and outside the plasma are interesting for various applications, such as possible laser acceleration of electrons up to the GeV range, high-energy short-duration particle sources, protron radiography, fast-ignition approach to inertial confinement fusion, etc.