This paper focuses on applications of shape memory alloys (SMAs) to deal with complex engineering problems. They come under the category of shape memory materials (SMMs). They can regain their original shape by heating above a specific critical temperature (shape memory effect), and they depict complete recovery of plastic strain induced by removing the applied stress under isothermal conditions (Superelasticity). This article presents a review of SMAs applications in the aerospace field highlighting wing morphing, variable geometry chevrons, smart wheels, rock splitters for space missions, variable area nozzles, and vortex generators. In the beginning, a general overview of SMAs is provided which includes the history of SMA development, general characteristics, and fabrication of SMAs. Subsequently, the design aspects of SMAs are discussed, along with the examination of diverse types of SMMs such as SMAs, SMPs, HTSMAs, and thin film SMAs. The deduced findings depict the significance of SMAs as smart materials. The transformation temperature for Shape memory alloys like NiTi goes up to about 100 °C and actuation stresses well beyond 200 MPa, thus rendering them suitable for aerospace components. Lightweight SMA-based actuation systems can even reduce the cost by 2-3%. The challenges related to the high weight associated with wing morphing technology can also be addressed. This review synthesizes data from some 150 papers and attempts to map emerging trends, along with the existing research gaps, which might provide a direction for future SMA applications in aerospace systems. Through further rigorous research, these SMAs have the potential to address the challenges posed by complex engineering scenarios.