There has been renewed interest in sociotechnical systems in the context of transitioning to a more sustainable society. While gains have been made in the qualitative understanding of sustainable transitions and sociotechnical systems, these approaches have not been well-operationalized. Given the importance of meeting future energy and environmental policy targets, there is need to develop predictive techniques and more robust methods to quantify and analyze sociotechnical systems undergoing rapid change and uncertainty due to sustainability pressures. Sustainability transitions depend on large-scale diffusion of technological and behavioral innovations on physical and virtual networked systems. Transitions can therefore be viewed as a subclass of diffusion phenomenon and subject to a range of mathematical and computational methods. We review, categorize, and critically assess methodological and theoretical approaches that integrate different aspects of sustainability, innovation, and complexity. We argue that these approaches should be adapted to improve our understanding of the behavior and dynamics of a broad range of sociotechnical systems to meet sustainability objectives. We therefore also make the conceptual link between complexity and sustainability as complimentary fields of research to inform policy and decision making to achieve more sustainable outcomes.