This paper studies a fourth emerging service model of cloud computing, Business Process as a Service (BPaaS). BPaaS is generating hype but it is under researched with a lack of clarity regarding how BPaaS differentiates itself from other service models and what opportunities and challenges it presents for management and organisations attempting to implement it. In this paper we examine the theoretical underpinnings of BPaaS with a view to developing an understanding of the potential value of adopting the BPaaS model and its implications for the realisation of business value from cloud computing. We develop the SEIFS framework (Situation, Elemental, Integration, Flexibility, and Scalability) to provide guidance in the classification of cloud services as BPaaS or otherwise and attempt to validate this framework by using a series of case studies based in Irish cloud computing firms. Our paper aims to contribute to the literature by addressing confusion in the classification of cloud services, and specifically BPaaS. We also provide insights for prospective BPaaS providers to factor into their service design and discuss how BPaaS can provide a competitive advantage. Finally, we identify and discuss a number of areas for future research.