The amount of data generated owing to the rapid development of the Smart Internet of Things is increasing exponentially. Traditional machine learning can no longer meet the requirements for training complex models with large amounts of data. Federated learning, as a new paradigm for training statistical models in distributed edge networks, alleviates integration and training problems in the context of massive and heterogeneous data and security protection for private data. Edge computing processes data at the edge layers of data sources to ensure low-data-delay processing; it provides high-bandwidth communication and a stable network environment, and relieves the pressure of processing massive data using a single node in the cloud center. A combination of edge computing and federated learning can further optimize computing, communication, and data security for the edge-Internet of Things. This review investigated the development status of federated learning and expounded on its basic principles. Then, in view of the security attacks and privacy leakage problems of federated learning in the edge Internet of things, relevant work was investigated from cryptographic technologies (such as secure multi-party computation, homomorphic encryption and secret sharing), perturbation schemes (such as differential privacy), adversarial training and other privacy security protection measures. Finally, challenges and future research directions for the integration of edge computing and federated learning are discussed.