This Chapter is devoted to various optimal control problems for systems admitting generalized (discontinuous) solutions. The main purpose is to define a class of trajectories (generally speaking, discontinuous ones) wide enough to include the optimal solution. The main result of this chapter shows that the class of generalized solutions introduced for the description of discontinuous trajectories does indeed contain the optimal path. In other words, this class serves well as a class of generalized curves (by analogy with the same concept in classical optimal control theory). Later, we consider the generalized solutions in problems with state constraints. Two concepts of admissible solution are introduced, namely those of strong solution and weak solution. Strong solutions satisfy the state constraints “strictly,” that is, constraint viola-tions during the action of the impulse control are not allowed. On the contrary, the concept of weak solution admits constraint violations, but on the infinitesimally brief time interval when the impulse control acts. These two concepts lead to different types of trajectories, which require different tools of investigation. It is shown that by using the discontinuous time change it is possible to formulate two different equivalent auxiliary problems with ordinary controls. With the aid of the solutions of these auxiliary problems one can easily derive the solutions for the original problems. Moreover, in this Chapter we consider the optimal control problem for a hybrid system with possible state discontinuities. Here we again express a jump in the state by means of the discontinuous time change and also for the case of unilateral constraints inherent to mechanical systems.