Since the pioneering work of Tajima and Dawson on the laser electron a
ccelerator, experiments on the excitation of high-amplitude plasma wav
es by beat-wave, photon wakefield and self-resonant wakefield have bee
n performed in plasmas and give evidence of electron acceleration in t
he range 1-100 MeV for distances of less than one centimetre. Electron
s, either from the plasma itself, or injected from outside, are accele
rated to these relativistic energies by the longitudinal electric fiel
d of the laser-excited plasma wave whose phase velocity is close to th
e speed of light. After a short survey of the excitation mechanism of
this relativistic plasma wave, the scaling laws which link the electri
c field of the plasma wave, the energy gain of accelerated electrons a
nd the acceleration length to the parameters of the laser will be reca
lled. Then, limits for the energy of accelerated electrons will be giv
en in the case of passing and trapped electrons as well as in the case
of wavebreaking. These classical results will be compared with recent
experimental results of electron acceleration in CO2 and Nd, beat-wav
e, as well as for self-resonant wakefield. Future experiments on photo
n wakefield will be discussed. Relevant work performed to improve the
energy gain of acceleration schemes such as light channelling by prefo
rmed plasmas or by relativistic effects will be discussed.