Think of Archimedes' screw, only sticking up tens of thousands of miles from the surface into the earth, carrying tons of space crap without the need for rocket or laser propulsion.
It's pretty heady stuff, because instead of a single string extending into the heavens, there are two "floppy" ones that form an ellipse, harnessing the rotation of the earth as a means to turn the elevator to propel things upwards. West Virginia University rocket scientists Leonardo Golubović and Steven Knudsen proposed it, and they think it just might work. Says PhysOrg.com:
The unique double rotating motion of looped strings could provide a mechanism for objects to slide up the elevator cable into outer space. The space elevator could launch satellites and spacecraft with humans, and even be used to host space stations and research posts.
If you want to grasp the science behind all this stuff—which I haven't even attempted to explain—I recommend you have a look at the PhysOrg story. Me, I'll just sit here, contemplating what an additional 10,000 miles of altitude will do for my fear of heights. [PhysOrg.com via KurzweilAI.net; painting by Dean Ellis from this 1981 Omni Magazine article reprint about a pretty ambitious space elevator not unlike, but definitely not exactly like, the one proposed above.]