Lyapunov functions underpin the stability analysis and controller synthesis for aerospace vehicles, from spacecraft attitude control to autonomous flight systems and UAV swarm coordination. This review discusses the development of computational Lyapunov function synthesis methods. Within this scope, it traces the evolution from traditional Sum-of-Squares (SOS) programming to artificial intelligence symbolic discovery technologies, prompted by the increasing complexity of nonlinear systems. Specifically, the following stages can be identified: computational relaxation methods constrained by polynomial templates; data-driven paradigms leveraging neural network-based empirical approximations; a... More >