Fairness in Federated Learning (FL) is emerging as a critical factor driven by heterogeneous clients’ constraints and balanced model performance across various scenarios. In this survey, we delineate a comprehensive classification of the state-of-the-art fairness-aware approaches from a multifaceted perspective, i.e., model performance-oriented and capability-oriented. Moreover, we provide a framework to categorize and address various fairness concerns and associated technical aspects, examining their effectiveness in balancing equity and performance within FL frameworks. We further examine several significant evaluation metrics leveraged to measure fairness quantitatively. Finally, we explore exciting open research directions and propose prospective solutions that could drive future advancements in this important area, laying a solid foundation for researchers working toward fairness in FL.