Since 1945, rock climbers have used nylon or perlon ropes (perlon is a European version of nylon). Nylon is both strong and durable. Modern nylon climbing ropes have a "kernmantle" or "jacketed-core" structure: a woven nylon sheath over a braided core.
The kernmantle design means that it’s possible to have a very "dynamic" rope: one with the ability to stretch a lot on impact. In fact, there are two categories of climbing rope: static and dynamic. A static rope will not stretch very much. For most rock climbing, you need a dynamic rope; the stretch in the rope will absorb some of the impact of a fall, reducing what could otherwise be a jarring or even back-breaking impact on your body. Static ropes are fine for rappelling, and for top-roping (which is when you are anchored in and/or being rappelled from above). Dynamic ropes work for these activities as well, but rappelling or top-roping with a dynamic rope will decrease the life span of the rope.
Most modern climbing ropes have similar dimensions. They are normally at least 50 meters (165 feet) long. They can be 9.5, 10, 10.5, or 11 millimeters in diameter.