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Over the recent years, with the increasing adoption of Federated Learning (FL) algorithms and growing concerns over personal data privacy, Privacy-Preserving Federated Learning (PPFL) has attracted tremendous attention from both academia and industry. Practical PPFL typically allows multiple participants to individually train their machine learning models, which are then aggregated to construct a global model in a privacy-preserving manner. As such, Privacy-Preserving Aggregation (PPAgg) as the key protocol in PPFL has received substantial research interest. This survey aims to fill the gap between a large number of studies on PPFL, where PPAgg is adopted to provide a privacy guarantee, and the lack of a comprehensive survey on the PPAgg protocols applied in FL systems. In this survey, we review the PPAgg protocols proposed to address privacy and security issues in FL systems. The focus is placed on the construction of PPAgg protocols with an extensive analysis of the advantages and disadvantages of these selected PPAgg protocols and solutions. Additionally, we discuss the open-source FL frameworks that support PPAgg. Finally, we highlight important challenges and future research directions for applying PPAgg to FL systems and the combination of PPAgg with other technologies for further security improvement.