Federated learning (FL) as a novel paradigm in Artificial Intelligence (AI), ensures enhanced privacy by eliminating data centralization and brings learning directly to the edge of the user’s device. Nevertheless, new privacy issues have been raised particularly during training and the exchange of parameters between servers and clients. While several privacy-preserving FL solutions have been developed to mitigate potential breaches in FL architectures, their integration poses its own set of challenges. Incorporating these privacy-preserving mechanisms into FL at the edge computing level can increase both communication and computational overheads, which may, in turn, compromise data utility and learning performance metrics. This paper provides a systematic literature review on essential methods and metrics to support the most appropriate trade-offs between FL privacy and other performance-related application requirements such as accuracy, loss, convergence time, utility, communication, and computation overhead. We aim to provide an extensive overview of recent privacy-preserving mechanisms in FL used across various applications, placing a particular focus on quantitative privacy assessment approaches in FL and the necessity of achieving a balance between privacy and the other requirements of real-world FL applications. This review collects, classifies, and discusses relevant papers in a structured manner, emphasizing challenges, open issues, and promising research directions.