Although the safety of prospective Maritime Autonomous Surface Ships will largely depend on their ability to detect potential hazards and react to them, the contemporary scientific literature lacks the analysis of how to achieve this. This could be achieved through an application of leading safety indicators. The aim of the performed study was to identify the research directions of leading safety indicators in three safety-critical operational aspects of Maritime Autonomous Surface Ships: collision avoidance, intact stability, and communication. To achieve this, literature review is performed, taking into account scientific documents including journal and conference papers. The results indicate that the need for establishing operational leading safety indicators is recognized by numerous scholars, who sometimes make suggestions of what the set of indicators shall consist of. Some leading safety indicators for autonomous vessels are readily identifiable in the scientific literature and used in current practice. However, the research effort is lacking a holistic approach to the issue.