The body of literature on business process compliance is large and approaches specifically addressing process monitoring are hard to identify. Moreover, proper means for the systematic comparison of these approaches are missing. Hence, it is unclear which approaches are suitable for particular scenarios. The goal of this paper is to define a framework for Compliance Monitoring Functionalities (CMF) that enables the systematic comparison of existing and new approaches for monitoring compliance rules over business processes during runtime. To define the scope of the framework, at first, related areas are identified and discussed. The CMFs are harvested based on a systematic literature review and five selected case studies. The appropriateness of the selection of CMFs is demonstrated in two ways: (a) a systematic comparison with pattern-based compliance approaches and (b) a classification of existing compliance monitoring approaches using the CMFs. Moreover, the application of the CMFs is showcased using three existing tools that are applied to two realistic data sets. Overall, the CMF framework provides powerful means to position existing and future compliance monitoring approaches.