The James Clerk Maxwell Telescope (JCMT) has been the world’s most successful single-dish telescope at submillimetre wavelengths since it began operations in 1987. From the pioneering days of single-element photometers and mixers, through to the state-of-the-art imaging and spectroscopic cameras, the JCMT has been associated with a number of major scientific discoveries. Famous for the discovery of ‘SCUBA’ galaxies, which are responsible for a large fraction of the far-infrared background, the JCMT has pushed the sensitivity limits arguably more than any other facility in this most difficult of wavebands in which to observe. Closer to home, the first images of huge discs of cool debris around nearby stars gave us clues to the evolution of planetary systems, further evidence of the importance of studying astrophysics in the submillimetre region. Now approaching the 30th anniversary of the first observations, the telescope continues to carry out unique and innovative science. In this review article, we look back on some of the major scientific highlights from the past 30 years.