Coherent x rays can be produced by scattering of laser light by a beam of relativistic electrons, provided that the electron beam is density modulated or the scattering is done at, or near, 90°. Since the coherent scattering is proportional to N2, where N is the number of electrons, and the incoherent scattering is proportional to N, also a modest degree of coherence can substantially increase the x-ray yield. The theory of laser-electron-beam scattering is reviewed and compared with the emission of radiation by an electron beam in an undulator. Examples of the practical implementation of an intense source of coherent x rays are discussed.