Paternoster elevators don't have doors or buttons. The run continuously in a loop, like a ferris wheel. When you reach your desired floor, you get off quickly. 99 Percent Invisible has an article about these curious conveyances, which can still be found in Europe.
The compartments of a paternoster lift wrap around like a chain, with two side-by-side openings on each level. Passengers step into and out of either the "up" or "down" side on a given floor.
These endlessly looping lifts are slower than conventional elevators, generally moving about one foot per second, which makes it possible to get on and off. Their slow-but-perpetual motion is the key ingredient to their efficiency: with so many compartments and no need to stop, passengers need never wait for a lift. Taken together, all of the small cars can also hold more people than a one-per-shaft system.