Illusory contours (IC) have attracted a considerable interest in recent years to derive models of how sensory information is processed and integrated within the visual system. In addition to various findings from neuropsychology, neurophysiology, and psychophysics, several recent studies have used functional neuroimaging to identify the cerebral substrates underlying human perception of IC (in particular Kanizsa figures). In this paper, we review the results from more than 20 neuroimaging studies on IC perception and highlight the great diversity of findings across these studies. We then provide a detailed discussion about the localization ('where' debate) and the timing ('when' debate) of IC processing as suggested by functional neuroimaging. Cortical responses involving visual areas as early as V1/V2 and latencies as rapid as 100 ms have been reported in several studies. Particular issues concerning the role of the right hemisphere and the retinotopic encoding of IC are also discussed. These different findings are tentatively brought together to propose different hypothetical cortical mechanisms that might be responsible for the visual formation of IC. Several remaining questions on IC processing that could potentially be explored with functional neuroimaging techniques are finally emphasized.