Business model innovation has seen a recent surge in academic research and business practice. Changes to business models are recognized as a fundamental approach to realize innovations for sustainability. However, little is known about the successful adoption of sustainable business models (SBMs). The purpose of this paper is to develop a unified theoretical perspective for understanding business model innovations that lead to better organizational economic, environmental and social performance. The paper examines bodies of literature on business model innovation, sustainability innovation, networks theory, stakeholder theory and product–service systems. We develop five propositions that support the creation of SBMs in a unified perspective, which lays a foundation to support organizations in investigating and experimenting with alternative new business models. This article contributes to the emerging field of SBMs, which embed economic, environmental and social flows of value that are created, delivered and captured in a value network. It highlights gaps for addressing the challenges of business model innovation for sustainability and suggests avenues for future research. © 2017 The Authors. Business Strategy and the Environment published by ERP Environment and John Wiley & Sons Ltd