What does fMRI tell us about neuronal activity?

In recent years, cognitive neuroscientists have taken great advantage of functional magnetic resonance imaging (fMRI) as a non-invasive method of measuring neuronal activity in the human brain. But what exactly does fMRI tell us? We know that its signals arise from changes in local haemodynamics that, in turn, result from alterations in neuronal activity, but exactly how neuronal activity, haemodynamics and fMRI signals are related is unclear. It has been assumed that the fMRI signal is proportional to the local average neuronal activity, but many factors can influence the relationship between the two. A clearer understanding of how neuronal activity influences the fMRI signal is needed if we are correctly to interpret functional imaging data.