Jerome Pearson, President of STAR, Inc., invented the space elevator in the early 1970s, when he was at the Air Force Research Laboratory at Wright-Patterson Air Force Base, Ohio. He published his ideas in an international journal that first brought the idea to the attention of the entire world of spaceflight researchers. Sir Arthur Clarke, living in Sri Lanka, consulted with Pearson in the late 1970s in writing his novel, "The Fountains of Paradise," which brought Pearson’s idea of the space elevator to an even larger audience. Sir Arthur included in the book an appendix that credited Pearson.

The idea of a "stairway to heaven" is as old as the Bible, and includes the Tower of Babel and Jacob’s Ladder. Modern thought on space elevators goes back to Konstantin Tsiolkovski, a school teacher in St. Petersburg, Russia, who did a "thought experiment" on a tower into space. Tsiolkovski imagined tall towers and cosmic railways, and discovered what we now call the geostationary altitude for a spacecraft, at which point the gravitational and centrifugal forces on a body in a one-day orbit are in balance. Tsiolkovski calculated the synchronous altitudes for the five visible planets, and the sun, but concluded that building such a real tower into orbit was impossible.
In the 1960s, Leningrad engineer Yuri Artsutanov discovered how to build a real structure for the space elevator, but published no technical papers; his ideas appeared in a Sunday supplement to Pravda, and their significance was not recognized in the West. In 1966, a group of oceanographers led by John Isaacs at the Scripps Institute of Oceanography, La Jolla, California, again discovered the concept. But they proposed such a thin wire that it would be cut by micro-meteorites almost instantly, and was therefore completely impractical.
Pearson, unaware of the earlier work, independently discovered the concept, but published it in the international journal Acta Astronautica, and thus gave the space elevator to the international aerospace community for the first time. His discovery included using the space elevator for zero-net-energy space launching, and for launching payloads from the elevator tip to reach other planets without requiring rockets. He also was first examine the dynamics of actually lifting payloads up the elevator, and found limitations on the speeds of ascent, akin to the critical velocities of a rotating shaft and the periodic loads from soldiers marching on a bridge.
Hans Moravec had been thinking along similar lines, and seeing the Pearson orbital tower publication led him to propose rotating space towers unconnected to a planet or moon, for catching and throwing space payloads to different orbits. Artsutanov had also proposed this concept earlier, but it was not known to Moravec.
Pearson later extended the space elevator idea to the moon, using the Lagrangian points as balance points in lieu of the geostationary orbit, and discovered that such a "lunar anchored satellite" could be used to bring lunar materials into high Earth orbit cheaply. Interestingly, Artsutanov published a paper on a lunar space elevator just one month later, without either author being aware of the other!

Paul Birch of England conceived of a dynamic space elevator, in the form of a hollow ring about the Earth with a super-orbital wire inside it. The resulting unbalanced centrifugal force would support shorter space elevators hanging from the ring, producing a low-altitude space elevator. Payloads could be lifted along the elevators to the orbital ring, and then accelerated to orbital velocity. Keith Lofstrom proposed a smaller launch loop with a moving conductor inside, to lift itself above the atmosphere and launch payloads into orbit. Rod Hyde of Lawrence Livermore Laboratory conceived of another dynamic space elevator, supported vertically by electromagnetic disks being fired from the base upward, and then deflected down by a magnetic driver at the top. The reaction force would keep the tower stable to any altitude, but of course payloads at the top would not have orbital velocity unless the tower reached at least synchronous altitude over the equator.
Paul Penzo then extended the idea of space elevators and tethers to Phobos, the closer the moon of Mars. He also proposed using a rotating tether to attach a spacecraft to asteroids, to change its orbit without rockets, like a gravitational assist. Pearson and Guy Pignolet of Germany almost simultaneously conceived of the idea of a rotating tube about an asteroid, to throw asteroidal material into space, providing rocket thrust to retrieve the asteroid. Another possibility is to use the Artsutanov-Moravec rotating tether to catch suborbital payloads and throw them into Earth orbit. The payloads could be launched either by rockets or by electromagnetic guns.
One fundamental problem of building the space elevator is the phenomenal strength of materials required to support its mass over the 35,800-km height to geostationary orbit. Artsutanov and Pearson recognized that carbon "whiskers" representing perfect-crystal structures, might be one way to achieve the required strength. When carbon nanotube structures were discovered, it was realized immediately by Richard Smalley at Rice University in Houston, Texas and by Boris Yakobson at North Carolina State University that these super-strength materials would make the space elevator possible.
Using these ideas and materials, Bradley Edwards proposed a practical scheme for constructing a space elevator about the Earth, and received NASA funding for a study. A workshop at NASA Marshall Space Flight Center produced a summary of the current state of the space elevator. However, it may still be a long time before such a space elevator is built about the Earth, because of its interference with all other Earth satellites. The orbit of any Earth satellite, except for geostationary satellites, would constantly intersect that of the space elevator structure, and would therefore require active avoidance.
On the other hand, it is possible to build Pearson’s lunar space elevator now, and use it to develop lunar resources and for lunar farside communication. It could also be constructed of existing composite materials, and does not require the super-strength of carbon nanotubes. The use of rotating tethers for asteroid retrieval is also possible now, and could even be used to rid the Earth of the danger of asteroid collisions, such as the one that killed the dinosaurs.
Jerome Pearson has also proposed an ingenious explanation for the negative results in the search for extraterrestrial intelligence (SETI). His concept is that the unusual presence of our large moon renders our system a "double planet," and has shaped Earth’s evolution and its ability to support life. He and his colleagues at STAR, Inc. have also proposed innovative techniques for Earth climate control, using asteroid resources and controlled EDDE spacecraft to provide an artificial ring about the Earth, like Saturn’s, to shade the Earth. References are listed here, in order of subject and approximate chronological order.
Tsiolkovski, K. E., Speculations of Earth and Sky, and On Vesta, (science fiction works,
  1895). Moscow, Izd-vo AN SSR, 1959.
Artsutanov, Y., "Into the Cosmos by Electric Rocket," Komsomolskaya Pravda, 31 July
  1960. (The contents are described in English by Lvov in Science, 158, 946-947, 1967.)
Isaacs, J., Vine, A. C., Bradner, H. and Bachus, G. E., "Satellite Elongation into a true
  Sky-Hook," Science 151, 682-683, 1966.
Pearson, J., "The Orbital Tower: A Spacecraft Launcher Using the Earth's Rotational
Acta Astronautica 2, 785-799, 1975.
Artsutanov, Y., "Into the Cosmos without Rockets," Znanije-Sila 7, 25, 1969.
Moravec, H., "A Non-Synchronous Rolling Skyhook," Journal of the Astronautical
25, 307-322, 1978.
Pearson, J., "Anchored Lunar Satellites for Cislunar Transportation and
Journal of the Astronautical Sciences, Vol. XXVII, No. 1,
  pp. 39-62, Jan/Mar 1979.
Pearson, J., "Lunar Anchored Satellite Test," AIAA Paper 78-1427, August 1978.
Artsutanov, Y., "Railway ‘Moon-Earth’," Technika Molodishi, No. 4, p. 21, 1979.
Clarke, A. C., The Fountains of Paradise, Harcourt Brace Jovanovich, New York, 1979.
Pignolet, G., "Retrieval of Asteroids for Space Materials," IAF Paper 79-F-122,
  September 1979.
Pearson, J. "Asteroid Retrieval by Rotary Rocket." AIAA Paper 80-0116, January 1980.
Birch, P. M.,"Orbital Ring Systems and Jacob's Ladders," JBIS 35, 475-497, 1982.
Hyde, R., Wood, L., McCarthy, J., and Minsky, M., "The Star Bridge: A Skyhook We
  Can Build Now," Lawrence Livermore National Laboratory unpublished report, 1982.
Penzo, P. A., "Tethers for Mars Space Operations," AAS Paper 84-174, July 1984.
Lofstrom, K., "The Launch Loop—A low-cost Earth-to-orbit Launch System,"
  AIM Paper 85-1368, 1985.
Pearson, J., "Low Cost Launch System and Orbital Fuel Depot," Acta Astronautica
  19, 315-310, 1989.
Pearson, J., "The Moon and SETI," Acta Astronautica, Vol. 26, No. 3/4, pp. 151-155,
Yakobson, B. I., and Smalley, R. E., "Fullerene Nanotubes: C1,00,000 and Beyond,"
  American Scientist, Vol. 85, 324-337, July-August 1997.
Pearson, J., "Konstantin Tsiolkovski and the Origin of the Space Elevator,"
  IAF-97-IAA.2.1.09, 48th IAF Congress, Torino, Italy, October 6-10, 1997.
Smitherman, D. V., Jr., Compiler, The Space Elevator: An Advanced Earth-Space
  Infrastructure for the New Millennium
, Proceedings of a NASA
  Workshop, June 8-10 1999, NASA/CP-2000-210429, Marshall Space
  Flight Center, Huntsville, AL, August 2000.
Pearson, J., Oldson, J., and Levin, E., "Earth Rings for Planetary Environment Control,"
  IAF-02-U.1.01, 53rd IAFCongress, Houston, TX, 10-19 October 2002.
Edwards, B. C., and Westling, E. A., The Space Elevator: A Revolutionary
  Earth-to-Space Transportation System
, ISBN 0972604502, published by the
  authors, January 2003.