A morphing aircraft can be defined as an aircraft that changes configuration to maximize its performance at radically different flight conditions. These configuration changes can take place in any part of the aircraft, e.g. fuselage, wing, engine, and tail. Wing morphing is naturally the most important aspect of aircraft morphing as it dictates the aircraft performance in a given flight condition, and has been of interest to the aircraft designers since the beginning of the flight, progressing from the design of control surfaces to the variable-sweep wing. Recent research efforts (mainly under DARPA and NASA sponsorships) however, are focusing on even more dramatic configuration changes such as 200% change in aspect ratio, 50% change in wing area, 5o change in wing twist, and 20o change in wing sweep to lay the ground work for truly multi-mission aircraft. Such wing geometry and configuration changes, while extremely challenging, can be conceptually achieved in a variety of ways - folding, hiding, telescoping, expanding, and contracting a wing, coupling and decoupling multiple wing segments, etc. These concepts can be classified under a few 'independent' categories and sub-categories so as to permit a systematic evaluation of benefits and challenges. This paper presents: 1) a review of prior work leading to current R&D efforts, 2) classification of morphing designs, and 3) a summary of technical challenges encountered in designing a morphing aircraft.