PurposeThe purposes of this paper are: (1) to identify what types of business process operation controllers are discussed in literature and how can they be classified in order to establish the available body of knowledge in the literature, and then, (2) to identify which concepts are relevant for business process operation control and how are these concepts related in order to offer a reference model for assessing how well are control layers enforced in the dynamic stable nature of an enterprise' business processes operation.Design/methodology/approachOne cycle of the circular framework for literature review as proposed by Vom Brocke et al. (2009) is followed. Five stages are comprised: (1) definition of review scope (Section 1 and 2), (2) conceptualization of topic (Section 3), (3) literature search (Section 4), (4) literature analysis and synthesis (Section 5), and (5) definition of a research agenda (Section 6 that also concludes the paper). Vom Brocke, J., Simons, A., Niehaves, B., Niehaves, B., Reimer, K., Plattfaut, R., and Cleven, A. (2009), “Reconstructing the giant: on the importance of rigour in documenting the literature search process”, ECIS 2009 Proceedings, Vol. 161.FindingsResults indicate that (1) many studies exist in the literature, but no integrated knowledge is proposed, hindering the advance of knowledge in this field, (2) a knowledge gap exists between the implemented solutions and the conceptualization needed to generalize the solution to other contexts. Also, the ontology proposed provides a reference model for assessing the maturity of the business process control operation.Research limitations/implicationsThe contents contained in the paper needs to be further deepened to include the concepts of “business process management” and “business process mining”, as well as a semantic equivalence study between concepts can integrate better this conceptual framework and identify similarities. Then, the relationship between industries and dynamically stable business processes operation concepts have not yet been fully investigated. Thirdly, the atypical curve of interest that business processes operational control has been receiving in literature is not fully understood.Practical implicationsSome example applications that could benefit from this ontology are (1) security policy for business processes fine grained access control; (2) business processes enforced with decentralized policies, e.g. blockchain; (3) business process compliance and change; or (4) intelligent enterprise decision-making process, e.g. using AI trained neural network to support the human decision to choose if a control actuation is positive or negative instead of relying only on human-based decisions.Social implicationsWe understand that business process operation is a dynamically stable system, where steady motion is achieved with the continuous imposition of actor's actions. Therefore, all the work that contribute to the development of knowledge regarding the actor's actions in their execution environment offer the ability to optimize, and/or reengineering, business processes delivering more social value or better social conditions.Originality/valueIn the best of our knowledge this work is unique in the sense that integrates a set of concepts that is rarely, or never, combined. Table 3 corroborates this result.