DSG, or Direct Shift Gearbox, is a form of paddle-shift system, used by Volkswagen Group companies under various names.
The principles of how it works go back to before the Second World War, but VW has perfected it for modern use. It has two clutches. As you select one gear, the next is primed to cut in as soon as you tap a paddle behind the steering wheel or nudge a lever on the floor. It’s particularly smooth in operation and very efficient.
There’s also a fully-automatic programme, but it's not entirely jolt-free.