Laser-driven plasma-based accelerators, which are capable of supporting fields in excess of $100\mathrm{GV}∕\mathrm{m}$, are reviewed. This includes the laser wakefield accelerator, the plasma beat wave accelerator, the self-modulated laser wakefield accelerator, plasma waves driven by multiple laser pulses, and highly nonlinear regimes. 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 diffraction, electron dephasing, laser pulse energy depletion, and 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 with preformed density channels. Instabilities relevant to intense short-pulse laser-plasma interactions, such as Raman, self-modulation, and hose instabilities, are discussed. Experiments demonstrating key physics, such as the production of high-quality electron bunches at energies of $0.1–1\mathrm{GeV}$, are summarized.

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