Neuroscientists typically assume that human mental functions are generated by the brain and that its structural elements, including the different cell layers and tissues that form the neocortex, play specific roles in this complex process. Different functional units are thought to complement one another to create an integrated self-awareness or episodic memory. Still, findings that pertain to brain dysplasia and brain lesions indicate that in some individuals there is a considerable discrepancy between the cerebral structures and cognitive functioning. This seems to question the seemingly well-defined role of these brain structures. This article provides a review of such remarkable cases. It contains overviews of noteworthy aspects of hydrocephalus, hemihydranencephaly, hemispherectomy, and certain abilities of "savants." We add considerations on memory processing, comment on the assumed role of neural plasticity in these contexts, and highlight the importance of taking such anomalies into account when formulating encompassing models of brain functioning.