In a plasma, some of the energy of a high-power laser beam can be transferred to a longitudinal plasma wave with a high phase velocity. This wave can in turn accelerate relativistic charged particles to very high energies. Several mechanisms have been proposed to generate these intense electric fields and some of them have already been tested experimentally. Using the beat wave method, electric fields of 1 - 10 have been produced and electrons have been accelerated with an energy gain from 1 MeV to more than 30 MeV. Some preliminary experiments have shown that electrons can be accelerated in plasma waves generated by the wakefield method. In the case of self-modulated wakefield, electric fields larger than 100 trap electrons and eject them from the plasma with an energy up to 100 MeV. The perspectives in the near future are the production of intense and short electron beams of a few MeV and the acceleration of electrons up to 1 GeV. To reach an energy of 1 TeV and get closer to the parameters required by the high-energy physicists, one will have to test some new methods to be able to guide the laser beam over large distances.