Different from the centralized deep learning mode, distributed deep learning gets rid of the limitation that the data must be centralized during the model training process, which realizes the local operation of the data, and allows all participants to collaborate without exchanging data. It significantly reduces the risk of user privacy leakage, breaks the data island from the technical level, and improves the efficiency of deep learning. Distributed deep learning can be widely used in smart medical care, smart finance, smart retail and smart transportation. However, typical attacks such as generative adversarial network attacks, membership inference attacks and backdoor attacks, have revealed that distributed deep learning still has serious privacy vulnerabilities and security threats. This paper first compares and analyzes the characteristics of the three distributed deep learning modes and their core problems, including collaborative learning, federated learning and split learning. Secondly, from the perspective of privacy attacks, it comprehensively expounds various types of privacy attacks faced by distributed deep learning, and summarizes the existing privacy attack defense methods. At the same time, from the perspective of security attacks, the paper analyzes the attack process and inherent security threats of the three security attacks: data poisoning attacks, adversarial sample attacks, and backdoor attacks, and analyzes the existing security attack defense technology from the perspectives of defense principles, adversary capabilities, and defense effects. Finally, from the perspective of privacy and security attacks, the future research directions of distributed deep learning are discussed and prospected.