The desmodromic valve, invented by Gustav Mees in 1907, and first produced for a commercial available engine from 1933 to 1934 by a company called Azzariti. The first time that Ducati produced a desmodromic valve system was in 1956 for the Ducati 125 Grand Prix motorcycle.
Desmodromic valve operation uses a cam to close the engine's valves as well as to open them. There are a few design variations, but essentially, there's one rocker arm on top of the valve that runs on a conventional camshaft to open the valve. But there is another opposed rocker arm which pulls the valve up again against its seat.
This opposed rocker arm is operated by a weirdly-shaped cam, which has a much larger lobe. As the camshafts turn, the opening cam pushes the valve move. When it's time for the valve to close, the profile of the closing cam pushes the closing rocker arm back up against the valve lifter, as the opening cam profile moves the closing rocker away from the valve, letting it move back up against its seat. Light springs are used to help the valves seat, but the valve's motion is essentially down to the cam profiles.
The advantages of desmodromic valves are better valve control at high engine speeds as well as potentially faster valve opening speeds. They're only communally used by Ducati, which owns a bunch of desmo valve patents although they didn't invent the desmo system.