In 2008, Vian reported an increasing interest in understanding how corruption affects healthcare outcomes and asked what could be done to combat corruption in the health sector. Eleven years later, corruption is seen as a heterogeneous mix of activity, extensive and expensive in terms of loss of productivity, increasing inequity and costs, but with few examples of programmes that have successfully tackled corruption in low-income or middle- income countries. The commitment, by multilateral organisations and many governments to the Sustainable Development Goals and Universal Health Coverage has renewed an interest to find ways to tackle corruption within health systems. These efforts must, however, begin with a critical assessment of the existing theoretical models and approaches that have underpinned action in the health sector in the past and an assessment of the potential of innovations from anticorruption work developed in sectors other than health. To that end, this paper maps the key debates and theoretical frameworks that have dominated research on corruption in health. It examines their limitations, the blind spots that they create in terms of the questions asked, and the capacity for research to take account of contextual factors that drive practice. It draws on new work from heterodox economics which seeks to target anticorruption interventions at practices that have high impact and which are politically and economically feasible to address. We consider how such approaches can be adopted into health systems and what new questions need to be addressed by researchers to support the development of sustainable solutions to corruption. We present a short case study from Bangladesh to show how such an approach reveals new perspectives on actors and drivers of corruption practice. We conclude by considering the most important areas for research and policy.