This work presents the application of optimal control strategies to pumped storage power plants (PSPPs). Four main aspects are considered here: optimal stationary operation, optimal power control, optimal plant shutdown, and optimal electricity market operation. A detailed and computationally efficient plant model is developed in the first step as the basis for these tasks. The developed models are used to study the optimal stationary operation of PSPPs. A special focus is given to heterogeneous plants containing combinations of fixed- and variable-speed generators. The power control is achieved by means of a nonlinear model predictive control-based strategy. This control strategy consists of a stationary optimizer for optimal quasi-stationary operation, a model predictive controller (MPC) for optimal closed-loop performance, and an extended Kalman filter (EKF) to estimate non-measurable states and parameters. Simulation studies show that the control strategy allows for fast following of set-point changes while allowing for safe plant operation by systematically considering all system constraints within the MPC. The dynamic performance in a plant shutdown is also studied by developing optimal (nonlinear) guide vane closing laws. Finally, the optimal market operation of PSPPs in different electricity markets is studied. A reduced-order model, which contains all necessary effects, is developed in the first step. This model is used to study the performance of PSPPs in the Day-Ahead and Ancillary services markets. A moving horizon optimization for the Intraday market is developed subsequently. Finally, a robust optimization-based bidding curve generation strategy to generate offer and demand curves in the Day-Ahead market is developed in the last step.