Generation of human induced pluripotent stem cells (hiPSCs) and their differentiation into a variety of cells and organoids have allowed setting up versatile, non-invasive, ethically sustainable, and patient-specific models for the investigation of the mechanisms of human diseases, including viral infections and host–pathogen interactions. In this study, we investigated and compared the infectivity and replication kinetics in hiPSCs, hiPSC-derived neural stem cells (NSCs) and undifferentiated neurons, and the effect of viral infection on host innate antiviral responses of representative flaviviruses associated with diverse neurological diseases, i.e., Zika virus (ZIKV), West Nile virus (WNV), and dengue virus (DENV). In addition, we exploited hiPSCs to model ZIKV infection in the embryo and during neurogenesis. The results of this study confirmed the tropism of ZIKV for NSCs, but showed that WNV replicated in these cells with much higher efficiency than ZIKV and DENV, inducing massive cell death. Although with lower efficiency, all flaviviruses could also infect pluripotent stem cells and neurons, inducing similar patterns of antiviral innate immune response gene expression. While showing the usefulness of hiPSC-based infection models, these findings suggest that additional virus-specific mechanisms, beyond neural tropism, are responsible for the peculiarities of disease phenotype in humans.