In this Chapter, we derive a series of necessary and sufficient optimality conditions for generalized solutions. We use the following general methodology, first suggested by B.Mille in 1982-1984: • the original optimal control problem with unbounded controls and which admits generalized (discontinuous) solutions is reformulated in the equivalent form of an auxiliary optimization problem with bounded controls; the correspondence between these problems is established with the aid of the discontinuous time change; • in the new auxiliary problem the necessary optimality conditions are formulated in the form of the maximum principle; • finally, these conditions are transformed into optimality conditions for the original problem by means of the inverse time transformation. This methodology was used for the derivation of sufficient optimality conditions in the maximum principle form [M.Milltr, 1969] and for the derivation of dynamic programming equations [M.Motta, 1996]. We use it to obtain optimality conditions in optimal control problems with state constraints, in hybrid systems, and in linear-convex problems with state constraints. In linear and linear-convex problems this generalized maximum principle gives necessary and sufficient optimality conditions. Moreover, we use the presented methodology to derive necessary optimality conditions in hybrid systems with unilateral constraints.