Originally conceived in 1895 by Konstantin Tsiolkovsky, and inspired by the Eiffel Tower, the concept of the space elevator is a radical one. Essentially proposing a tether stretching from an anchor on the Earth into a low geostationary orbit, it would allow the conveyance of materials and personnel into space without the need for rockets.
If this could be achieved, then space exploration would take a giant leap ahead, enabling materials to be lifted into low orbit quickly and cheaply, and the building of a space port and building yard for inter-planetary ships. With the coming end of the life of the space shuttle, with limited viable alternatives (NASA has recently awarded contracts to two private companies to undertake haulage to the space station), interest in the space elevator has regained momentum, with an annual conference pushing the proposal forward.
At the most recent conference, a slightly madly ingenius idea of how to get centrifugal force to drive the elevator, rather than powering the lifts directly, was presented by Age-Raymond Riise of the European Space Agency.
More info on the space elevator can be found here. Information on the 'X-Prize'-like competition for the space elevator may be found here and on the LiftPort Group here.
In the twenty-first century, answers may yet be found in nineteenth century ideas.