This report treats some theoretical and numerical aspects of optimal control and the theory of differential games applied to missile guidance problems. Such issues are important at several defferent levels of missile control, from low level stabilization and tracking problems in controller design to high level mission planning problems. A list of such application areas are given. After a relatively elementary derivation of the maximum principle, a number of less well known results of optimal control are given. In particular this leads to an understanding of why the indirect Hamiltonian methods of optimal control have bad numerical properties for typical path planning problems, and that hence direct numerical optimization methods are called for. The following chapters study such numerical schemes. Methods for path planning are treated in chapter 3. A method is proposed, using a Voronoi grid based method to generate an initial path candidate, from which a local optimum is found by Newton´s method. The main application is avoidance of threat regions, such as hostile SAM sites. In chapter 4, a differential game is studied, where two missiles fight each other. Here angular limitation of the seeker is taken into account. For this optimization problem, a receding horizon approach is attempted.