  Laser-driven plasma accelerators provide acceleration gradients three orders
of magnitude greater than conventional machines, offering the potential to
shrink the length of accelerators by the same factor. To date,
laser-acceleration of electron beams to particle energies comparable to those
offered by synchrotron light sources has been demonstrated with plasma
acceleration stages only a few centimetres long. This article describes the
principles of operation of laser-driven plasma accelerators, and reviews their
development from their proposal in 1979 to recent demonstrations. The potential
applications of plasma accelerators are described and the challenges which must
be overcome before they can become a practical tool are discussed.
