The analysis of animal models of neurological disease has been instrumental in furthering our understanding of neurodevelopment and brain diseases. However, animal models are limited in revealing some of the most fundamental aspects of development, genetics, pathology, and disease mechanisms that are unique to humans. These shortcomings are exaggerated in disorders that affect the brain, where the most significant differences between humans and animal models exist, and could underscore failures in targeted therapeutic interventions in affected individuals. Human pluripotent stem cells have emerged as a much-needed model system for investigating human-specific biology and disease mechanisms. However, questions remain regarding whether these cell-culture-based models are sufficient or even necessary. In this review, we summarize human-specific features of neurodevelopment and the most common neurodevelopmental disorders, present discrepancies between animal models and human diseases, demonstrate how human stem cell models can provide meaningful information, and discuss the challenges that exist in our pursuit to understand distinctively human aspects of neurodevelopment and brain disease. This information argues for a more thoughtful approach to disease modeling through consideration of the valuable features and limitations of each model system, be they human or animal, to mimic disease characteristics.