In this talk I will present a class of infinite horizon optimal control problems subject to semilinear parabolic equations. Existence of a solution, first and second order optimality conditions are obtained in the presence of constraints on the controls, which can be either pointwise in space-time, or pointwise in time and $L^2$ in space. These results rely on a new $L^\infty$ estimate for nonlinear parabolic equations in an essential manner. Finally, the approximation by finite horizon control problems is considered.