Superconducting cavities have been in operation in accelerators for 25 years. In the last decade many installations in storage rings and linacs have been completed. Meanwhile, nearly 1 km of active cavity length is in operation in accelerators. Large-scale applications of superconducting radiofrequency systems are planned for future e + e − linear colliders and proton linacs. Superconducting cavities have been proved to operate at higher gradient, lower AC power demand and more favourable beam dynamics conditions than comparable normal conducting resonators. The performance of the best single-cell cavities comes close to the intrinsic limitation of the superconducting material. Complete multicell structures with all auxiliaries (couplers, tuner, etc) lag behind in performance because of their complexity. In this paper, an overview of accelerators with superconducting cavities is given. Limitations of superconducting performance are described and research and development efforts towards understanding and curing these effects are discussed in detail. Fundamentals of superconductivity and radiofrequency cavity design are briefly explained.