Fixed-wing aircraft is a term used to refer to monoplanes, biplanes and triplanes, in fact all conventional aircraft that are neither balloons, airships, autogyros, helicopters or tilt-rotors. The term embraces a minority of aircraft that have folding wings, intended to fold when on the ground, perhaps to ease stowage or facilitate transport on, for example, a vehicle trailer or the powered lift connecting the hangar deck of an aircraft carrier to its flight deck. It also embraces an even smaller number of aircraft, such as the General Dynamics F-111 Aardvark and the Panavia Tornado, that can fold their wings during flight. In the early days of their development, these were termed "variable geometry" aircraft. When the wings of these aircraft are fully swept, usually for high speed cruise, the trailing edges of their wings abut the leading edges of their tailplanes, giving an impression of a single delta wing if viewed from above or below.

Sir George Cayley, the inventor of the science of aerodynamics, was building and flying models of fixed wing aircraft as early as 1803, and he built a successful passenger-carrying glider in 1853, but the first practical self-powered airplanes were designed and constructed by the Wright brothers. Their first successful test flights were in 1903, and by 1904 the Flyer III was capable of fully-controllable stable flight for substantial periods. Strictly, its wings were not completely fixed, as it depended for stability on a flexing mechanism named wing warping. This was soon superseded by the competitive development of ailerons, attached to an otherwise rigid wing.