Down syndrome (DS), caused by triplication of chromosome 21, is the most frequent aneuploidy observed in the human population and represents the most common genetic form of intellectual disability and early-onset Alzheimer’s disease (AD). Individuals with DS exhibit a wide spectrum of clinical presentation, with a number of organs implicated including the neurological, immune, musculoskeletal, cardiac, and gastrointestinal systems. Decades of DS research have illuminated our understanding of the disorder, however many of the features that limit quality of life and independence of individuals with DS, including intellectual disability and early-onset dementia, remain poorly understood. This lack of knowledge of the cellular and molecular mechanisms leading to neurological features of DS has caused significant roadblocks in developing effective therapeutic strategies to improve quality of life for individuals with DS. Recent technological advances in human stem cell culture methods, genome editing approaches, and single-cell transcriptomics have provided paradigm-shifting insights into complex neurological diseases such as DS. Here, we review novel neurological disease modeling approaches, how they have been used to study DS, and what questions might be addressed in the future using these innovative tools.