Brain organoids are self-assembled three-dimensional aggregates generated from pluripotent stem cells with cell types and cytoarchitectures that resemble the embryonic human brain. As such, they have emerged as novel model systems that can be used to investigate human brain development and disorders. Although brain organoids mimic many key features of early human brain development at molecular, cellular, structural and functional levels, some aspects of brain development, such as the formation of distinct cortical neuronal layers, gyrification, and the establishment of complex neuronal circuitry, are not fully recapitulated. Here, we summarize recent advances in the development of brain organoid methodologies and discuss their applications in disease modeling. In addition, we compare current organoid systems to the embryonic human brain, highlighting features that currently can and cannot be recapitulated, and discuss perspectives for advancing current brain organoid technologies to expand their applications.