The work of Euler and Lagrange on the three-body problem have marked a contribution of paramount importance in Celestial Mechanics and Astrodynamics through the discovery of the existence of equilibrium positions in the synodic reference frame. The positions which are collinear with the location of the primaries are shown to be unstable; nevertheless, they can be used to construct orbits that find many applications in space missions, giving rise to the modern field of Astrodynamics called Space Manifold Dynamics. In this context, control and optimization problems play a prominent role and allow one to design new and efficient space trajectories.