A space elevator cable rotates along with the rotation of the Earth. Earth's rotation creates upward centrifugal force on the counterweight. The counterweight is held down by the cable while the cable is held up and taut by the counterweight. The base station anchors the whole system to the surface of the Earth. Climbers climb up and down the cable with cargo.

Since the maximum stress on a space elevator cable is at geosynchronous altitude, the cable must be thickest there and taper as it approaches the surface of the Earth. The cable must be made of a material with a large tensile strength/density ratio as a material with very high strength and lightness is needed. Also, it would be useful if the cable’s chemical properties enabled it to conduct electricity so that electric power could be transmitted to the rider and the orbiting station.

Carbon is a good strong, light material because it has very few of the nucleons that contribute most of the dead weight of any material, but has high inter-atomic bonding forces due to its outer electrons. 

The challenge remains to extend to macroscopic sizes the production of carbon fibers. The current (2009) carbon nanotube technology allows growing tubes up to just a few tens of centimeters.