The Rogallo wing is a flexible type of wing. In 1948, Francis Rogallo, a NASA engineer, and his wife Gertrude Rogallo, invented a self-inflating flexible wing they called the Parawing, also known after them as the "Rogallo Wing" and flexible wing. NASA considered Rogallo's flexible wing as an alternative recovery system for the Mercury and Gemini space capsules, and for possible use in other spacecraft landings, but the idea was dropped from Gemini in 1964 in favor of conventional parachutes.

Rogallo had been interested in the flexible wing since 1945. He and his wife built and flew kites as a hobby. They could not find official backing for the wing, including at Rogallo's employer National Advisory Committee for Aeronautics (NACA), so they carried out experiments in their own time. By the end of 1948 they had two working designs using a flexible wing — a kite they called "Flexi-Kite" and a gliding parachute they later referred to as a "paraglider". Rogallo and his wife received a patent on a flexible square wing in March 1951. Selling the Flexi-kite as a toy helped to finance their work and publicize the design.

In the late 1950s and early 1960s, U.S. aerospace manufacturers worked on parachute designs for space capsule recovery. NASA briefly considered the Rogallo wing to replace the traditional round parachute for the Project Mercury capsule during temporary development problems. Later, the Rogallo wing was the initial choice for the Project Gemini capsule, but development problems ultimately forced its replacement with the parachute.

Nowadays the term "Rogallo wing" is synonymous with one composed of two partial conic surfaces with both cones pointing forward. Slow Rogallo wings have wide, shallow cones. Fast subsonic and supersonic Rogallo wings have long, narrow cones. The Rogallo wing is a simple and inexpensive flying wing with remarkable properties. The wing itself is not a kite, nor can it be characterized as glider or powered aircraft, until the wing is tethered or arranged in a configuration that glides or is powered. In other words, how it is attached and manipulated determines what type of aircraft it becomes. The Rogallo wing is most often seen in toy kites, but has been used to construct spacecraft parachutes, sport parachutes, ultralight powered aircraft like the trike and hang gliders. Rogallo had more than one patent concerning his finding; the due-diligence expansion of his invention involved cylindrical formats, multiple lobes, various stiffenings, various nose angles, etc. The Charles Richards design and use of the Rogallo wing in the NASA Paresev project resulted in an assemblage that became the stark template for the standard Rogallo hang-glider wing that would blanket the world of the sport in the early 1970s.

Beyond that, the wing is designed to bend and flex in the wind, and so provides favorable dynamics analogous to a spring suspension. Flexibility allows the wing to be less susceptible to turbulence and provides a gentler flying experience than a similarly sized rigid-winged aircraft. The trailing edge of the wing – which is not stiffened – allows the wing to twist, and provides aerodynamic stability without the need for a tail (empennage).

In 1961–1962, aeronautical engineer Barry Palmer foot-launched several versions of a framed Rogallo wing hang glider to continue the recreational and sporting spirit of hang gliding. Another player in the continuing evolution of the Rogallo wing hang glider was James Hobson whose "Rogallo Hang Glider" was published in 1962 in the Experimental Aircraft Association's magazine Sport Aviation, as well as shown on national USA television in the Lawrence Welk Show. Later in Australia John Dickenson in mid-1963, set out to build a controllable waterskiing kite/glider, which he admitted adapting from a Ryan Aeronautical flex-wing aircraft. Publicity from the Paresev tested-and-flown hang gliders and the various space contractors sparked interest in the Rogallo-promoted wing design among several amateur designersin: Thomas H. Purcell Jr., Barry Hill Palmer, James Hobson, Mike Burns, John Dickenson, Richard Miller, Bill Moyes, Bill Bennett, Dave Kilbourne, Dick Eipper and many others. A renaissance in hang gliding occurred in the 1960s, and John Worth was the early leader in the pack of four-boom hang glider builders and designers using public domain designs.

Single-point hang was fully demonstrated in Breslau in 1908, as well as the triangle control frame that would later be seen in NASA's and John Worth's hang gliders and powered hang gliders. Thomas Purcell and Mike Burns would use the triangle control frame. Much later Dickenson would do similarly as he fashioned an airframe to fit on the by-then standard four boom stiffened Rogallo wing. Dickenson's model made use of a single hang point and an A frame: He started with a framed Rogallo wing airfoil with a U-frame (later an A-frame control bar) to it; it was composed of a keel, leading edges, a cross-bar and a fixed control frame. Weight-shift was also used to control the glider. The flexible wing – called "Ski Wing" – was first flown in public at the Grafton Jacaranda Festival in September 1963 by Rod Fuller while towed behind a motorboat.

The Australian Self-Soar Association states that the first foot-launch of a hang glider in Australia was in 1972. In Torrance, California, Bill Moyes was assisted in a kited foot-launch by Joe Faust at a beach slope in 1971 or 1972. Moyes went on to build a company with his own trade-named Rogallo wing hang gliders that used the trapeze control frame he had seen in Dickenson's and Australian manned flat-kite ski kites. Bill Moyes and Bill Bennett exported new refinements of their own hang gliders throughout the world. The parawing hang glider was inducted into the Space Foundation Space Technology Hall of Fame in 1995.^{[citation needed]}