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Observing present scarcity of fossil fuel and emissions of greenhouse gases, electricity generated from Renewable Energy (RE) sources turns out to be the best alternative for generating the power. In RE system, the inverter is normally used to condition the DC power into AC to meet the requirements of load and transmission system. The inverter offers myriad benefits; however, the presence of harmonics (particularly low-order) in the output voltage affects the efficiency and performance of inverter, causes switching losses and decreases the lifetime of the system. In last three decades, significant research has been done to develop the efficient control technique for eliminating the unwanted harmonics. The preliminary review of existing control techniques revealed that the selective harmonic elimination pulse-width modulation (SHEPWM) is more proficient to eliminate the low-order harmonics. However, non-linear transcendental equations used in this technique pose a challenge to solve particularly for calculus-based methods. With the advent of powerful and low-cost computers, bio-inspired intelligent algorithms (BIAs) seem to be a better approach for solving these complex equations. This review paper presents the detailed principle operation of nine well-known BIAs and discusses their application in inverters for harmonic elimination (HE). Moreover, different objective functions are also discussed in this paper which is used by the researchers for HE. Additionally, the performance of five renowned BIAs, namely, Imperialist Competitive Algorithm, Particle Swarm Optimization, Differential Evolution, Bee Algorithm and Genetic Algorithm is critically evaluated. Their performance is analyzed in terms of accuracy, computational complexity, convergence speed, and a number of control parameters. The conclusion has been made on the basis of information extracted from the literature and evaluation results with future recommendations. This single paper covers all the essential information regarding HE in inverters, which will help researchers to design the efficient RE conversion system. [ABSTRACT FROM AUTHOR]