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Global trends such as just-in-time, containerization, and e-commerce have led to an ever increasing freight volume to be transported under tight delivery schedules. Many supply chains, thus, apply fully-automated sorting systems as one basic component of their distribution processes. Examples range from baggage handling in airports, over parcels sorted by tilt tray conveyors in distribution centers of the postal service industry, up to batches of picking orders isolated in the warehouses of e-commerce retailers. This paper surveys the scientific literature on all kinds of fully-automated conveyor-based sorting systems from an operational research perspective. We describe the wide range of applications and their different sorting systems, define their joint decision problems to be solved when designing and operating a sorter, review the literature, and identify future research challenges.