To support the whole business process compliance lifecycle, one also needs to monitor the actual processes and not just check their design. Recently, many approaches have been proposed that utilize a broad range of constraint languages and techniques to realize compliance monitoring solutions. Due to this diversity, the comparison of existing approaches is difficult and consequently hampers the evaluation of which approaches are suitable for which application scenarios. This paper provides a framework to compare and evaluate existing compliance monitoring approaches. The framework is based on ten typical Compliance Monitoring Functionalities (CMFs). These have been derived using a systematic literature review and five case studies from different domains. Existing approaches are evaluated based on the CMF framework, resulting in a list of open questions and a discussion of new challenges in this field.