Artificial Intelligence (AI) has demonstrated remarkable capabilities in domains such as recruitment, finance, healthcare, and the judiciary. However, biases in AI systems raise ethical and societal concerns, emphasising the need for effective fairness testing methods. This paper reviews current research on fairness testing, particularly its application through search-based testing. Our analysis highlights progress and identifies areas of improvement in addressing AI systems' biases. Future research should focus on leveraging established search-based testing methodologies for fairness testing. © 2023 IEEE.