Functional neuroimaging using MRI relies on measurements of blood oxygen level-dependent (BOLD) signals from which inferences are made about the underlying neuronal activity. This is possible because neuronal activity elicits increases in blood flow via neurovascular coupling, which gives rise to the BOLD signal. Hence, an accurate interpretation of what BOLD signals mean in terms of neural activity depends on a full understanding of the mechanisms that underlie the measured signal, including neurovascular and neurometabolic coupling, the contribution of different cell types to local signalling, and regional differences in these mechanisms. Furthermore, the contributions of systemic functions to cerebral blood flow may vary with ageing, disease and arousal states, with regard to both neuronal and vascular function. In addition, recent developments in non-invasive imaging technology, such as high-field fMRI, and comparative inter-species analysis, allow connections between non-invasive data and mechanistic knowledge gained from invasive cellular-level studies. Considered together, these factors have immense potential to improve BOLD signal interpretation and bring us closer to the ultimate purpose of decoding the mechanisms of human cognition. This theme issue covers a range of recent advances in these topics, providing a multidisciplinary scientific and technical framework for future work in the neurovascular and cognitive sciences. This article is part of the theme issue 'Key relationships between non-invasive functional neuroimaging and the underlying neuronal activity'.