When considering what makes us human, the development of the neocortex, the seat of our higher cognitive abilities, is of central importance. Throughout this complex developmental process, neocortical stem and progenitor cells (NSPCs) exert a priming role in determining neocortical tissue fate, through a series of cellular and molecular events. In this Perspective article, we address five questions of relevance for potentially human-specific aspects of NSPCs, (i) Are there human-specific NSPC subtypes? (ii) What is the functional significance of the known temporal differences in NSPC dynamics between human and other great apes? (iii) Are there functional interactions between the human-specific genes preferentially expressed in NSPCs? (iv) Do humans amplify certain metabolic pathways for NSPC proliferation? and finally (v) Have differences evolved during human evolution, notably between modern humans and Neandertals, that affect the performance of key genes operating in NSPCs? We discuss potential implications inherent to these questions, and suggest experimental approaches on how to answer them, hoping to provide incentives to further understand key issues of human cortical development.