Origins
Most climbing historians credit the development of the rappel to Jean Estéril Charlet, a French climber based in Chamonix. Charlet developed the technique of abseiling (as it is know in the rest of the world), and used it first while descending from the Petit Dru in 1876.
Dulfersitz
The Dulfersitz rappel was invented by German mountain climber Hans Dülfer around the turn of the 19th century. With the Dulfersitz, the climber straddles the rope, then brings the rope up around his back and over his shoulder, and holds on to it with the hand near the hip.
Geneva Rappel
The Geneva rappel is a modified Dulfersitz, with the hip and arm wrapped around the rope. It has less control than the Dulfersitz.
Carabiner Brake
The carabiner brake rappel became the standard rappel setup in the 1960s and was especially popular because it didn't require additional equipment. A carabiner brake uses four to six carabiners, with the carabiners set up with their gates opposed to that the rope won't slip through both to create friction.
Modern Devices
By the 1980s, rappel devices, such as the Figure 8 and had come into vogue. The 1990s saw the introduction of smaller, lighter tube-style devices that provided more friction such as the Black Diamond ATC.