Optimal control problems are also defined by the maximization of a functional but are constrained instead by an ordinary differential equation and some other side constraints. This chapter contains (necessary) conditions for an optimum according to the Pontriyagin’s maximum principle, when several types of initial or terminal side constraints, both over the independent and dependent variables, are present. It is applied to both optimal distributional problems, as the optimal taxation problem subjected to an incentive compatibility constraint (the Mirrlees problem), and to intertemporal optimization problems, as in benchmark optimal capital accumulation, household consumption and savings, and small benchmark dynamic general equilibrium models.