[en] A key component of any particle accelerator is the device that imparts energy gain to the charged particle. This is usually an electromagnetic cavity resonating at a microwave frequency, chosen between 100 and 3000 MHz. Serious attempts to utilize superconductors for accelerating cavities were initiated more than 25 years ago with the acceleration of electrons in a lead-plated resonator at Stanford University (1). The first full-scale accelerator, the Stanford SCA, was completed in 1978 at the High Energy Physics Laboratory (HEPL) (2). Over the intervening one and a half decades, superconducting cavities have become increasingly important to particle accelerators for nuclear physics and high energy physics. For continuous operation, as is required for many applications, the power dissipation in the walls of a copper structure is quite substantial, for example, 0.1 megawatts per meter of structure operating at an accelerating field of 1 million volts/meter (MV/m). since losses increase as the square of the accelerating field, copper cavities become severely uneconomical as demand for higher fields grows with the higher energies called for by experimenters to probe ever deeper into the structure of matter. Rf superconductivity has become an important technology for particle accelerators. Practical structures with attractive performance levels have been developed for a variety of applications, installed in the targeted accelerators, and operated over significant lengths of time. Substantial progress has been made in understanding field and Q limitations and in inventing cures to advance performance. The technical and economical potential of rf superconductivity makes it an important candidate for future advanced accelerators for free electron lasers, for nuclear physics, and for high energy physics, at the luminosity as well as at the energy frontiers