Three very different methods of accomplishing the same task - managing the operation of the transmission system in the deregulated power system operating environment - have been implemented as deregulated market structures have been created around the world. They are first, the optimal power flow (OPF) model found in various implementations in the United Kingdom, parts of the United States, and in Australia and New Zealand. Second, the point tariff, price area congestion control model used in the Nordpool market area in Norway and Sweden. Third, the U.S. transaction-based model. All are pragmatic solutions implemented in advance of complete theoretical understanding. Each has strengths and flaws, and there are some surprising inter-relationships. Each maintains power system security but differs in its impact on the economics of the energy market. No clearly superior method has so far emerged. In the future, methods of combining decentralized market solutions with operational use of optimal power flow may provide better solutions to existing and emerging problems.