The first rappelling (also known as abseiling) occurred in the 1870s in the French Alps. Hempen ropes were used then, far from having the dynamic and lightness properties of our current ropes.
The idea is to pass a rope around a rock, so that the two ends of the same rope are hanging over the sheer drop. The alpinist then rope down along the two parts of the rope. The rope goes between his shoulder and his waist in order to slow down the descent. Once on the bottom level, the alpinists simply pulls one of the two ends to recover the entire rope (hence the term rappelling, from the French rappel, recalling the rope).
From the sixties onwards, abseil devices are used to mitigate the friction on a metallic part linked to a harness by carabiner. Typical abseiling heights are 30 to 40 meters in alpinism or climbing, and may go on from relay zone to relay zone. The descents of some vertical shafts may take 180 meters in spelunking (cavings).
Climbing ropes are colored and very dynamic (thanks to some elastic properties, they are able to absorb falls), whereas spelunking ropes are white and static in order to make for an easier climbing up.