The human brain is often described as the most complex organ in our body. Because of the limited accessibility of living brain tissue, human-specific features of neurodevelopment and disease remain largely unknown. The ability of induced pluripotent stem cells to self-organize into 3D brain organoids has revolutionized approaches to studying brain development in vitro. This review will first look at the history of studying neural development in a dish and how organoids came to be. We evaluate the ability of brain organoids to recapitulate key developmental events, focusing on the generation of various regional identities, cytoarchitecture, cell diversity, features of neuronal maturation, and circuit formation. We also consider the limitations of the model and review recent approaches to improve reproducibility and the healthy maturation of brain organoids. Copyright © 2020 Cold Spring Harbor Laboratory Press; all rights reserved.