Cerebral organoids, three-dimensional cultures that model organogenesis, provide a new platform to investigate human brain development. High cost, variability, and tissue heterogeneity limit their broad applications. Here, we developed a miniaturized spinning bioreactor (SpinΩ) to generate forebrain-specific organoids from human iPSCs. These organoids recapitulate key features of human cortical development, including progenitor zone organization, neurogenesis, gene expression, and, notably, a distinct human-specific outer radial glia cell layer. We also developed protocols for midbrain and hypothalamic organoids. Finally, we employed the forebrain organoid platform to model Zika virus (ZIKV) exposure. Quantitative analyses revealed preferential, productive infection of neural progenitors with either African or Asian ZIKV strains. ZIKV infection leads to increased cell death and reduced proliferation, resulting in decreased neuronal cell-layer volume resembling microcephaly. Together, our brain-region-specific organoids and SpinΩ provide an accessible and versatile platform for modeling human brain development and disease and for compound testing, including potential ZIKV antiviral drugs.