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Participants in the supply and demand sides of electricity markets can potentially exercise their market power for their benefits. Hence, market power mitigation is an essential component of market management that physically and economically benefits operators by ensuring fairness in deregulated electricity markets. However, the mechanisms of mitigating market power in electricity markets pose several challenges in terms of market structure monitoring, market power evaluation, and market power mitigation. Therefore, this study provides a comprehensive analysis of market power mitigation mechanisms in electricity markets. First, a review of market structure monitoring and market power evaluation methods is provided to assess participants' potential and degree of use/abuse of market power. Then, a detailed review of optimal bidding strategies in the supply and demand sides of electricity markets is provided. Accordingly, a systematic classification of market power mitigation is described. Finally, market power mitigation challenges and potential future research directions are discussed.