The application of robust estimation methods to the power system state estimation problem was investigated. Techniques using both nonlinear and combinatorial optimization were considered, based on the requirements that the method developed should be statistically robust, and fast enough to be used in a real-time environment. Some basic concepts from robust statistics are introduced. The various estimation methods considered are reviewed, and the implementation of the selected estimator is described. Simulation results for several IEEE test systems are included. Other applications of the proposed technique, such as leverage point identification in large sparse systems, and robust meter placement are described. / Ph. D.