With the rapid demand of data and computational resources in deep learning systems, a growing number of algorithms to utilize collaborative machine learning techniques, for example, federated learning, to train a shared deep model across multiple participants. It could effectively take advantage of the resources of each participant and obtain a more powerful learning system. However, integrity and privacy threats in such systems have greatly obstructed the applications of collaborative learning. And a large amount of works have been proposed to maintain the model integrity and mitigate the privacy leakage of training data during the training phase for different collaborative learning systems. Compared with existing surveys that mainly focus on one specific collaborative learning system, this survey aims to provide a systematic and comprehensive review of security and privacy researches in collaborative learning. Our survey first provides the system overview of collaborative learning, followed by a brief introduction of integrity and privacy threats. In an organized way, we then detail the existing integrity and privacy attacks as well as their defenses. We also list some open problems in this area and opensource the related papers on GitHub: https://github.com/csl-cqu/awesome-secure-collebrative-learning-papers.