It has been shown that prolonged exposure to a human face leads to shape-selective visual aftereffects. It seems that these face-specific aftereffects (FAEs) have multiple components, related to the adaptation of earlier and higher level processing of visual stimuli. The largest magnitude of FAE, using long-term adaptation periods, is usually observed at the retinotopic position of the preceding adaptor stimulus. However, FAE is also detected, to a smaller degree, at other retinal positions in a spatially invariant way and this component depends less on the adaptation duration. Several lines of evidences suggest that while the position-specific FAE involves lower level areas of the ventral processing stream, the position-invariant FAE depends on the activation of higher level face-processing areas and the fusiform gyrus in particular. In the present paper, we summarize the available behavioural, electrophysiological and neuroimaging results regarding the spatial selectivity of FAE and discuss their implications for the visual stability of object representations across saccadic eye movements.