A great number of countries' electricity industries have been deregulated since 1990s, and more and more countries are going to do that. Electricity industry is one of the most complex systems in the world because of its special physical characteristics. The electricity industry has been vertically integrated in the past 100 years, that is, generation, transmission and distribution are all controlled by regulated public utilities. With the development of new electricity technology, especially the invention of CCGT, deregulation of electricity industry becomes feasible. After deregulation, generation and transmission are separated. The generators are required to bid in the wholesale electricity market for their production while the transmission networks are still controlled by regulated independent system operator because of its network effect. After the deregulation, the electricity price continues to stay unexpectedly high because of generators' market power. In fact, the generators' market power has become one of the most important problems in the deregulated electricity industries. As is known to all, the final result of the generators' market power is high price, which is not necessarily the result of market power. Sometimes the high price is probably due to high demand and low supply, that is the scarcity rents. The generators' market power should be suppressed while scarcity rent is necessary to the generators, by which the generators can recover their large scale fixed costs, though the scarcity rent should be protected. How to differentiate the market power from scarcity rent has become a challenging but meaningful work. Though it is hard work to monitor the generators' market power because of the complexity of electricity system, there are still plenty of achievements in this field. In this paper, we review the literature on the monitoring of generators' market power in wholesale electricity market by monitoring. In traditional industrial economics, market concentration index is the most commonly used method to measure market power, but not appropriate to be applied to electricity market because of its special characteristics. As we know, electricity demand and supply are highly inelastic and insensitive to the price, so the generators share high market power during the peak period even if its market share is very small. Some economists try to perfect the concentration index to reflect the characters of electricity market, which are pivotal supplier indicator and residual supply index, but these indices are still static and not ideal. More complex methods are simulation models, including competitive benchmark analysis, Cournot simulation and supply function equilibrium simulation. Simulation models try to reflect the main characters of the electricity market and simulate the generators' market behaviors in special conditions. The results of the simulation model is more accurate but complex. Besides the behavior indices, other three methods are also considered, including residual demand analysis, new empirical industrial organization and withhold analysis. These methods try to reflect the characters of electricity market and thus complex too. [ABSTRACT FROM AUTHOR]