In recent years, federated learning has received widespread attention as a technology to solve the problem of data islands, and it has begun to be applied in fields such as finance, healthcare, and smart cities. The federated learning algorithm is systematically explained from three levels. First, federated learning is defined through the definition, architecture, classification of federated learning, and comparison with traditional distributed knowledge. Then, based on machine learning and deep learning, the current types of federated learning algorithms are classified, compared, and analyzed in-depth. Finally, the communication from the perspectives of cost, client selection, and aggregation method optimization, the federated learning optimization algorithms are classified. Finally, the current research status of federated learning is summarized. Finally, the three major problems and solutions of communication, system heterogeneity, and data heterogeneity faced by federated learning are proposed and expectations for the future.