Ensuring that business processes adhere to the rules imposed on them is the goal of business process compliance (BPC). The source for those rules are mainly laws, guidelines, or regulations, and consequently, BPC bridges the gap between the legal and the process domain. BPC can be structured into three phases: design-time, run-time and auditing. During each of those phases different data sources, ranging from process models to event logs, event streams and natural language texts such as process descriptions or regulatory documents, are of interest. This diversity of data sources and BPC phases requires a broad range of methods and techniques. In this keynote paper, selected approaches addressing the research vision of working towards holistic BPC are presented. Furthermore, current limitations and directions for future work are outlined, for example, how to ensure compliance of processes under changing laws and how to mitigate effects of changes to restore compliance.