Governments in some of the world’s richest nations appear to be caught in a double challenge of declining social budgets even as social needs are increasing. In this context, Outcomes Based Commissioning (OBC), has been suggested as one way in which ‘more’ social services can be provided for ‘less’ public resources. This form of commissioning is often linked with a new financing tool for social services, referred to in the US as ‘Pay for Success and Payment by Results in the UK or as a ‘Social Impact Bond’ (SIB). However, to date, this approach is under-theorised and this is a limiting factor both for shaping a research and evaluation agenda around SIBs and in understanding how such instruments might develop in future. Without a theoretical rationale for SIBs, it is not straightforward to assess whether, and how well, they have achieved their goals, and how they might be developed further. In this paper we consider two broad approaches to theorising SIBs. One draws on public administration theories, the other on innovation theories. To date, SIBs have often been theorised as the logical next step in the New Public Management (NPM). But NPM itself is a contested theory and recent theoretical innovations in public administration, particularly the concept of New Public Governance might provide a more useful theoretical framework. A second broad approach through which to understand SIBs is their potential to improve the rate and dissemination of innovation. There are many different innovation models that might be applied to better understanding of SIBs. We look first at the concept of Open Innovation with its focus on distributed innovation processes in which knowledge flows across organisational boundaries and more recent articulations – Open Innovation 2.0 – which place greater emphasis on mixed economy collabarations involving: industry; government; universities; and communities and users (the so-called ‘quadruple helix’) to solve societal challenges. We go on to consider social innovation, with its clearer focus on using social means to deliver social outcomes and whether SIBs can be theorised through this lens. No one model is entirely satisfactory as an explanatory framework for SIBs and we conclude by suggesting that a supporting theory combining NPG with elements of Open Innovation 2.0 and social innovation might be a productive approach for shaping future research and, in addition, might suggest some future directions for the next generation of SIBs.