Over the past few years this exciting concept has been steadily moving towards reality. When it does happen - and I believe it will - it will be a milestone in man's development.
Basically it involves putting a very large satellite or asteroid into geostationary orbit (so it appears fixed over one place on Earth like many satellites) and dropping a cable down to earth. This cable is then used by elevators to haul material and possible people up to orbit - slowly, safely and very cheaply. Like a railroad to the heavens...
The technology does not quite exist yet especially a cable strong enough but many feel the challenges can be over come. Research is being done and companies have been set up to build elevators. There is now an prize and annual competition to test the technology for short cables.
It would also seem to be energy efficient and friendly to the environment - the elevators might even be solar powered from collectors on the satellite.
National Space Society Special Interest Chapter for the Space Elevator