We address the intractable problem of flexibility in business process management: how to deal with variations, unique cases and exceptions? We identify and characterise five conceptualisations of business process. We discuss the main elements and relationships, contracts, and existential and representational properties established by each conceptualisation. For each conceptualisation, we analyse how it impacts flexibility and discuss different strategies for increasing flexibility. Finally, we synthesise our findings in an integrated framework, which helps by relating different conceptualisations of business process with strategies to increase flexibility. This paper makes several conceptual and practical contributions. Considering the former, we disentangle various notions of business process, considering in particular differences between ex ante and ex post, and class and instance. We also highlight that flexibility requires integrating variety and a multi-view over the events defined by a process. Regarding contributions to practice, we propose a framework for organisations to analyse how business processes can be related to flexibility.