Amodal completion is the phenomenon of perceiving completed objects even though physically they are partially occluded. In this review, we provide an extensive overview of the results obtained from a variety of neuroimaging studies on the neural correlates of amodal completion. We discuss whether low-level and high-level cortical areas are implicated in amodal completion; provide an overview of how amodal completion unfolds over time while dissociating feedforward, recurrent, and feedback processes; and discuss how amodal completion is represented at the neuronal level. The involvement of low-level visual areas such as V1 and V2 is not yet clear, while several high-level structures such as the lateral occipital complex and fusiform face area seem invariant to occlusion of objects and faces, respectively, and several motor areas seem to code for object permanence. The variety of results on the timing of amodal completion hints to a mixture of feedforward, recurrent, and feedback processes. We discuss whether the invisible parts of the occluded object are represented as if they were visible, contrary to a high-level representation. While plenty of questions on amodal completion remain, this review presents an overview of the neuroimaging findings reported to date, summarizes several insights from computational models, and connects research of other perceptual completion processes such as modal completion. In all, it is suggested that amodal completion is the solution to deal with various types of incomplete retinal information, and highly depends on stimulus complexity and saliency, and therefore also give rise to a variety of observed neural patterns.