Psychologists use Functional Magnetic Resonance Imaging (fMRI) to view the brain 'in action', measuring changes in blood flow that identify which regions are used to, for example, remember words, perceive pain or engage emotions.  The statistical methodology of these brain mapping studies, however, depends on mass-univariate linear modelling, a rich and stable suite of tools for fitting and making inference on brain image data.  I will review the standard mass-univariate analysis methods and highlight their shortcomings, in particular their inability to explicitly model the spatial structure of the fMRI signals.  I will present a hierarchical spatial model for multi-subject fMRI analyses, where latent population- and individual-centres fit the focal signals.  The model uses priors for identifiability and full posterior sampling to provide inference on a variety of measures of interest unavailable in a mass-univariate framework, including population prevalence of activation and inter-subject spread of activation about population centres.  I show evaluations of the model with simulations and demonstrate it with real data.