Power generation system largely depends on fossil fuels to generate electricity. Due to various reasons, the reserves of fossil fuels are declining and will become too expensive in near future. At the same time, generation of power from fossil fuels causes hazardous gases and particulates to emit, which pollutes the air and causes significant and long term damages on the environment. For this reason, extensive research works have been conducted for last few decades from different perspectives to reduce both the fuel cost as well as the emission of hazardous gases in power generation system. This power generation problem is commonly referred to as the combined economic emission dispatch (CEED) problem. This paper provides a comprehensive review on the uses of different optimization techniques to solve CEED problem. Authors have found advanced nature-inspired methods as the most suitable and successful, and have concluded combinational hybrid methods as the most prospective methods to solve CEED problem.