Cognitive neuroscience depends on the use of blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI) to probe brain function. Although commonly used as a surrogate measure of neuronal activity, BOLD signals actually reflect changes in brain blood oxygenation. Understanding the mechanisms linking neuronal activity to vascular perfusion is, therefore, critical in interpreting BOLD. Advances in cellular neuroscience demonstrating differences in this neurovascular relationship in different brain regions, conditions or pathologies are often not accounted for when interpreting BOLD. Meanwhile, within cognitive neuroscience, the increasing use of high magnetic field strengths and the development of model-based tasks and analyses have broadened the capability of BOLD signals to inform us about the underlying neuronal activity, but these methods are less well understood by cellular neuroscientists. In 2016, a Royal Society Theo Murphy Meeting brought scientists from the two communities together to discuss these issues. Here, we consolidate the main conclusions arising from that meeting. We discuss areas of consensus about what BOLD fMRI can tell us about underlying neuronal activity, and how advanced modelling techniques have improved our ability to use and interpret BOLD. We also highlight areas of controversy in understanding BOLD and suggest research directions required to resolve these issues.This article is part of the themed issue ‘Interpreting BOLD: a dialogue between cognitive and cellular neuroscience’.