Since the discovery of the neutron in 1934 neutron beams have been used in a very broad range of applications, As an aging fleet of nuclear reactor sources is retired the use of compact accelerator-driven neutron sources (CANS) are becoming more prevalent. CANS are playing a significant and expanding role in research and development in science and engineering, as well as in education and training. In the realm of multidisciplinary applications, CANS offer opportunities over a wide range of technical utilization, from interrogation of civil structures to medical therapy to cultural heritage study. This paper aims to provide the first comprehensive overview of the history, current status of operation, and ongoing development of CANS worldwide. The basic physics and engineering regarding neutron production by accelerators, target-moderator systems, and beam line instrumentation are introduced, followed by an extensive discussion of various evolving applications currently exploited at CANS.