Can space elevators be moved from the realm of the theoretical into the realm of the practical?
In the last few years a lot of interest has been generated in this question by the discovery of two new materials (in addition to carbon nanotubes) that are strong enough to build a space elevator: Hexagonal Boron Nitride and in particular Single Crystal Graphene. Graphene is currently the leading candidate because lower-strength versions are already being manufactured in kilometer lengths.
The latest developments will be discussed at the annual Space Elevator Conference in Chicago on Saturday and Sunday, September 7-8, hosted by the International Space Elevator Consortium (ISEC). See the ISEC website for details.
Image: Recent special issues of British Interplanetary Society publications devoted to the space elevator. The full articles are available at this link.