Practically relevant problems often involve complicated systems of partial differential equations for which numerical optimal control methods were close to being out of reach. Hence, the need of for developing novel techniques emerges. Suboptimal control strategies based on proper orthogonal decomposition (POD) guarantee reasonable performance of the controlled plant while being computationally tractable. In this talk error estimates for Galerkin-POD methods for linear and certain nonlinear parabolic systems are presented. Moreover, POD is utilized to solve open and closed loop optimal control problems for the Burgers equation. The relative simplicity of the equation allows comparison of POD-based algorithms with numerical results obtained from finite element discretization of the optimality system. For closed loop control suboptimal state feedback strategies are presented.