Understanding the impact of viral pathogens on the human central nervous system (CNS) has been challenging due to the lack of viable human CNS models for controlled experiments to determine the causal factors underlying pathogenesis. Human embryonic stem cells (ESCs) and, more recently, cellular reprogramming of adult somatic cells to generate human induced pluripotent stem cells (iPSCs) provide opportunities for directed differentiation to neural cells that can be used to evaluate the impact of known and emerging viruses on neural cell types. Pluripotent stem cells (PSCs) can be induced to neural lineages in either two- (2D) or three-dimensional (3D) cultures, each bearing distinct advantages and limitations for modeling viral pathogenesis and evaluating effective therapeutics. Here we review the current state of technology in stem cell-based modeling of the CNS and how these models can be used to determine viral tropism and identify cellular phenotypes to investigate virus-host interactions and facilitate drug screening. We focus on several viruses (e.g., human immunodeficiency virus (HIV), herpes simplex virus (HSV), Zika virus (ZIKV), human cytomegalovirus (HCMV), SARS-CoV-2, West Nile virus (WNV)) to illustrate key advantages, as well as challenges, of PSC-based models. We also discuss how human PSC-based models can be used to evaluate the safety and efficacy of therapeutic drugs by generating data that are complementary to existing preclinical models. Ultimately, these efforts could facilitate the movement towards personalized medicine and provide patients and physicians with an additional source of information to consider when evaluating available treatment strategies.