Astrocytes have a central role in brain development and function, and so have gained increasing attention over the past two decades. Consequently, our knowledge about their origin, differentiation and function has increased significantly, with new research showing that astrocytes cultured alone or co-cultured with neurons have the potential to improve our understanding of various central nervous system (CNS) diseases, such as Amyotrophic lateral sclerosis, Alzheimer’s disease or Alexander disease. The generation of astrocytes derived from pluripotent stem cells (PSCs) opens up a new area for studying neurologic diseases in vitro; these models could be exploited to identify and validate potential drugs by detecting adverse effects in the early stages of drug development. However, as it is now known that a range of astrocyte populations exist in the brain, it will be important in vitro to develop standardized protocols for the in vitro generation of astrocyte subsets with defined maturity status and phenotypic properties. This will then open new possibilities for co-cultures with neurons and the generation of neural organoids for research purposes. The aim of this review article is to compare and summarize the currently available protocols and their strategies to generate human astrocytes from PSCs. Furthermore, we discuss the potential role of human-induced PSCs derived astrocytes in disease modeling.