Receding Horizon Control (also known as Model Predictive Control) in the sense of this talk is a method for obtaining a feedback-like approximately optimal control for an infinite horizon optimal control problem by iteratively solving a series of finite horizon problems. It can thus be seen as a model reduction method in time. The talk presents conditions under which rigorous statements on the infinite horizon performance of the resulting closed loop trajectory can be made. Stability issues of the closed loop are also briefly addressed. The applicability of the conditions will be illustrated by several examples, including recent results on the Fokker-Planck equation (based on joint work with A. Fleig). More generally, the practicability of the conditions for controlled PDE models depending on the structure of the cost function is discussed.