This study investigates the growing interest in introducing circular economy (CE) principles in the aircraft construction and airplane industry, which traditionally has a linear value chain. Due to the adverse effects of traditional techniques on the environment, there is a need to adopt more green approaches. In particular, the authors examine how the CE’s “Reduce, Reuse, recycle” can be implemented in practice within aerospace, for example, through laser additive manufacturing to repair spare parts and recycle composite materials. Issues of complex composite materials and regulation are overcome. Future research will need to explore recycling technology developments, life cycle assessment tools, and regulatory reforms that would facilitate the thermally safe recycling of composite materials. This review sheds light on the potential of a circular economy to reduce the environmental impacts of the aviation industry.