Brain organoids are three-dimensional neural aggregates derived from pluripotent stem cells through self-organization and recapitulate architectural and cellular aspects of certain brain regions. Brain organoids are currently a highly exciting area of research that includes the study of human brain development, function, and dysfunction in unprecedented ways. In this Review, we discuss recent discoveries related to the generation of brain organoids that resemble diverse brain regions. We provide an overview of the strategies to complement these primarily neuroectodermal models with cell types of non-neuronal origin, such as vasculature and immune cells. Recent transplantation approaches aiming to achieve higher cellular complexity and long-term survival of these models will then be discussed. We conclude by highlighting unresolved key questions and future directions in this exciting area of human brain organogenesis.