I review a number of fMRI studies that investigate the effects of repeating faces on responses in the fusiform face area (FFA). These studies show that repetition suppression (RS), as well as repetition enhancement (RE), are sensitive to multiple factors, including pre-existing stimulus representations, cognitive task, lag between repetitions and spatial attention. Parallel EEG studies provide additional constraints on the timing of these repetition effects. Together, the results suggest that RS is not a unitary phenomenon, but likely subsumes multiple mechanisms that operate under different conditions. These mechanisms of course need to relate to single-cell data and known physiological mechanisms; but to make further progress, I believe we need dynamical neural network models that relate these mechanisms to the properties of neural populations that are measured by fMRI and EEG data. One example model is sketched, in which RS reflects an acceleration of neural dynamics, owing to reduced prediction error within a recurrent visual processing hierarchy.