Abstract: Neurodegenerative diseases (NDs) are a group of debilitating neurological disorders that primarily affect elderly populations and include Alzheimer’s disease (AD), Parkinson’s disease (PD), Huntington’s disease (HD), and amyotrophic lateral sclerosis (ALS). Currently, there are no therapies available that can delay, stop, or reverse the pathological progression of NDs in clinical settings. As the population ages, NDs are imposing a huge burden on public health systems and affected families. Animal models are important tools for preclinical investigations to understand disease pathogenesis and test potential treatments. While numerous rodent models of NDs have been developed to enhance our understanding of disease mechanisms, the limited success of translating findings from animal models to clinical practice suggests that there is still a need to bridge this translation gap. Old World non-human primates (NHPs), such as rhesus, cynomolgus, and vervet monkeys, are phylogenetically, physiologically, biochemically, and behaviorally most relevant to humans. This is particularly evident in the similarity of the structure and function of their central nervous systems, rendering such species uniquely valuable for neuroscience research. Recently, the development of several genetically modified NHP models of NDs has successfully recapitulated key pathologies and revealed novel mechanisms. This review focuses on the efficacy of NHPs in modeling NDs and the novel pathological insights gained, as well as the challenges associated with the generation of such models and the complexities involved in their subsequent analysis.