The physics and technology of superconducting bearings is reviewed. Particular attention is given to the use of high-temperature superconductors (HTSs) in rotating bearings. The basic phenomenology of levitational forces is presented, followed by a brief discussion of the theoretical models that can be used for conceptual understanding and calculations. The merits of various HTS bearing designs are presented, and the behaviour of HTS bearings in typical situations is discussed. The article concludes with a brief survey of various proposed applications for HTS bearings.