Operational risks are increasingly prevalent and complex to manage in organisations, culminating in substantial financial and non-financial costs. Given the inefficiencies and biases of traditional manual, static and qualitative risk management practices, research has progressed to using data analytics to objectively and dynamically manage risks. However, the variety of operational risks, techniques and objectives researched is not well mapped across industries. This paper thoroughly reviews the emerging research area applying data analytics to operational risk management (ORM) within financial services (FS) and energy and natural resources (ENR). A systematic literature search resulted in 2,538 publications, from which detailed bibliometric and content analyses are performed on 191 studies of relevance. The literature is classified using a novel multi-layered framework, informing critical analyses of the analytics techniques and data employed. Five core themes emerge, relevant to practitioners, researchers, educators and students across any sector: risk identification, causal factors, risk quantification, risk prediction and risk decision-making. Generally, ENR studies focus on identifying causal factors and predicting specific incidents, whereas FS applications are more mature surrounding risk quantification. To conclude, the comprehensive review reveals areas where further research is needed to advance ORM within and beyond FS and ENR, in pursuit of improved decision-making.