Machine learning (ML) has been pervasively researched nowadays and it has been applied in many aspects of real life. Nevertheless, issues of model and data still accompany the development of ML. For instance, training of traditional ML models is limited to the access of data sets, which are generally proprietary; published ML models may soon be out of date without an update of new data and continuous training; malicious data contributors may upload wrongly labeled data that leads to undesirable training results; and the abuse of private data and data leakage also exit. With the utilization of blockchain, an emerging and swiftly developing technology, these problems can be efficiently solved. In this paper, we survey the convergence of collaborative ML and blockchain. Different ways of the combination of these two technologies are investigated and their fields of application are examined. Discussion on the limitations of current research and their future directions are also included.