The human cerebral cortex possesses distinct structural and functional features that are not found in the lower species traditionally used to model brain development and disease. Accordingly, considerable attention has been placed on the development of methods to direct pluripotent stem cells to form human brain-like structures termed organoids. However, many organoid differentiation protocols are inefficient and display marked variability in their ability to recapitulate the three-dimensional architecture and course of neurogenesis in the developing human brain. Here, we describe optimized organoid culture methods that efficiently and reliably produce cortical and basal ganglia structures similar to those in the human fetal brain in vivo. Neurons within the organoids are functional and exhibit network-like activities. We further demonstrate the utility of this organoid system for modeling the teratogenic effects of Zika virus on the developing brain and identifying more susceptibility receptors and therapeutic compounds that can mitigate its destructive actions.