Boosted by the needs in high-energy physics and nuclear physics and also multidisciplinary applications, high-intensity proton synchrotrons and accumulator rings have been developed quickly around the world over the last 30 years. New projects and plans are proposed with even higher beam power. The proton beam power has increased from less than 10 kW in the 1970s to about 1 MW level today, and the required beam power in the coming decade is a few MW. This article reviews the achievements in designing and constructing rapid cycling synchrotrons (RCSs) and accumulator rings (ARs) and the future development trends, principally on proton beams but also including heavy ion beams. It presents the evolution of RCS and AR machines, today's design philosophy, relevant accelerator physics, and also state-of-the-art accelerator technology.