The technique of electron backscatter Kikuchi diffraction patterns (BKDPs) in the scanning electron microscope is reviewed. The paper focuses mainly on the crystallographic applications of the technique, including discussions on point group and space group determination and strain analysis. Orientation microscopy is discussed but not reviewed. The geometrical configurations of BKDPs are reviewed in detail and the relationship between BKDPs and the technique of electron channelling patterns (ECPs) is explored briefly. Essential crystallography is discussed and methods of analysis of BKDPs to extract crystallographic information are analyzed in detail. Some important characteristics of diffraction contrast in BKDPs are analyzed with respect to the geometry of the technique, the dynamical theory of electron diffraction and crystallographic applications. Examples of the use of theoretical contrast in pattern interpretation are provided. Anomalous effects in BKDPs are analyzed in detail and ways of identifying anomalous contrast in practice are discussed. BKDPs included in the paper are zincblende (ZnS), silicon, germanium, GaAs, chalcopyrite (CuFeS2, TaTe4 and Er2Ge2O7.