The physics of plasma-based accelerators driven by short-pulse lasers is reviewed. This includes the laser wake eld accelerator, the plasma beat wave accelerator, the self-modulated laser wake-field accelerator, and plasma waves driven by multiple laser pulses. The properties of linear and nonlinear plasma waves are discussed, as well as electron acceleration in plasma waves. Methods for injecting and trapping plasma electrons in plasma waves are also discussed. Limits to the electron energy gain are summarized, including laser pulse diraction, electron dephasing, laser pulse energy depletion, as well as beam loading limitations. The basic physics of laser pulse evolution in underdense plasmas is also reviewed. This includes the propagation, self-focusing, and guiding of laser pulses in uniform plasmas and plasmas with preformed density channels. Instabilities relevant to intense short-pulse laser-plasma interactions, such as Raman, self-modulation, and hose instabilities, are discussed. Recent experimental results are summarized.