Existing process modelling notations ranging from Petri nets to BPMN have difficulties capturing the essential features of the domain under study. Process models often focus on the control flow, lacking an explicit, conceptually well-founded integration with real data models, such as ER diagrams or UML class diagrams. In addition, they essentially rely on the simplifying assumption that each process model focuses on a single, explicitly defined notion of case, representing the type of objects that are separately manipulated when the process is instantiated into actual executions. To overcome this key limitation, Object-Centric Behavioural Constraints (OCBC) models were recently proposed as a new notation where data and control-flow are described in a single diagram, and where their interconnection is exploited to elegantly capture real-life processes operating over a complex network of objects. In this paper, we illustrate the essential and distinctive features of the OCBC approach, and contrast OCBC with contemporary, case-centric notations. We then relate the approach to recent developments in the conceptual understanding of processes, events, and their constituents, introducing a series of challenges and points of reflections for the community.