Studies of the basic methods of collective acceleration, specifically,
the acceleration of charged particles by space-charge waves and unneu
tralized beams of charged particles in plasmas, are briefly reviewed.
At present, the following methods of the acceleration by space-charge
waves are undergoing intensive development: the plasma beat-wave accel
erator, the laser wake-field accelerator, and the plasma wake-field ac
celerator, in which the accelerating plasma wave is excited by a train
of relativistic electron bunches. The most important problems and the
results obtained are discussed.