The control of magnetization by electric current is a rapidly developing area motivated by a strong synergy between breakthrough basic research discoveries and industrial applications in the fields of magnetic recording, magnetic field sensors, spintronics, and nonvolatile memories. In recent years, the discovery of spin–orbit torque has opened a spectrum of opportunities to manipulate the magnetization efficiently. This article presents a review of the historical background and recent literature focusing on spin–orbit torques (SOTs), highlighting the most exciting new scientific results and suggesting promising future research directions. It starts with an introduction and overview of the underlying physics of spin–orbit coupling effects in bulk and at interfaces, and then describes the use of SOTs to control ferromagnets and antiferromagnets. Finally, the prospects for the future development of spintronic devices based on SOTs are summarized.