As more and more business processes are migrated into cloud-based runtimes, there is a need to manage their state to provide support for quality attributes such as elasticity, scalability and dependability. In this paper we discuss how the REST architectural style provides a sensible choice to manage and publish service compositions under the Platform as a Service paradigm. We define the design principles of RESTful business process management in the cloud and compare several architectural alternatives to support elastic processes which can be monitored and dynamically adapted to workload changes.