This work describes the physics of plasma waves and plasma accelerators. The superiority of plasma accelerators over conventional accelerators has generated renewed interest in these devices with the advent of ultra-fast laser technology. The ponderomotive force produced by ultra short laser pulses interacting with the plasma is considered and the resulting acceleration gradient is derived from first principles. Electron injection is described. Beam driven, including electron beam and proton beam, plasma waves are proposed as the future of high energy plasma accelerators.