Malformations of the human neocortex in development constitute a heterogeneous group of complex disorders, resulting in pathologies such as intellectual disability and abnormal neurological/psychiatric conditions such as epilepsy or autism. Advances in genomic sequencing and genetic techniques have allowed major breakthroughs in the field, revealing the molecular basis of several of these malformations. Here, we focus on those malformations of the human neocortex, notably microcephaly, and macrocephaly, where an underlying basis has been established at the level of the neural stem/progenitor cells (NPCs) from which neurons are directly or indirectly derived. Particular emphasis is placed on NPC cell biology and NPC markers. A second focus of this review is on experimental model systems used to dissect the underlying mechanisms of malformations of the human neocortex in development at the cellular and molecular level. The most commonly used model system have been genetically modified mice. However, although basic features of neocortical development are conserved across the various mammalian species, some important differences between mouse and human exist. These pertain to the abundance of specific NPC types and/or their proliferative capacity, as exemplified in the case of basal radial glia. These differences limit the ability of mouse models to fully recapitulate the phenotypes of malformations of the human neocortex. For this reason, additional experimental model systems, notably the ferret, non-human primates and cerebral organoids, have recently emerged as alternatives and shown to be of increasing relevance. It is therefore important to consider the benefits and limitations of each of these model systems for studying malformations of the human neocortex in development.