The CIDOC Conceptual Reference Model (CIDOC-CRM) is an ISO Standard ontology for the cultural domain that is used for enabling semantic interoperability between museums, libraries, archives and other cultural institutions. For leveraging CIDOC-CRM, several processes and tasks have to be carried out. It is therefore important to investigate to what extent we can automate these processes in order to facilitate interoperability. For this reason, in this paper, we describe the related tasks, and we survey recent works that apply machine learning (ML) techniques for reducing the costs related to CIDOC-CRM-based compliance and interoperability. In particular, we (a) analyze the main processes and tasks, (b) identify tasks where the recent advances of ML (including Deep Learning) would be beneficial, (c) identify cases where ML has been applied (and the results are successful/promising) and (d) suggest tasks that can benefit from applying ML. Finally, since the approaches that leverage both CIDOC-CRM data and ML are few in number, (e) we introduce our vision for the given topic, and (f) we provide a list of open CIDOC-CRM datasets that can be potentially used for ML tasks.