This paper is an overview of Optimal Control Problems (OCPs) for aerospace applications tackled via the indirect method and a particular Physics-Informed Neural Networks (PINNs) framework, developed by the authors, named Extreme Theory of Functional Connections (X-TFC). X-TFC approximates the unknown OCP solutions via the Constrained Expressions, which are functionals made up of the sum of a free-function and a functional that analytically satisfies the boundary conditions. Thanks to this property, the framework is fast and accurate in learning the solution to the Two-Point Boundary Value Problem (TPBVP) arising after applying the Pontryagin Minimum Principle. The applications presented in this paper regard intercept problems, interplanetary planar orbit transfers, transfer trajectories within the Circular Restricted Three-Body Problem, and safe trajectories around asteroids with collision avoidance. The main results are presented and discussed, proving the efficiency of the proposed framework in solving OCPs and its low computational times, which can potentially enable a higher level of autonomy in decision-making for practical applications.