Invasive species are organisms like plants, animals, or microbes (e.g., fungi, bacteria, viruses) that are introduced to areas outside their historical or current distributions, most often through human‐mediated activity, and successfully establish populations that continue to reproduce and spread quickly. Collectively, invasive species are recognized as a major driver of global change that can pose a significant threat to ecosystems, economies, and human health. Concerns about invasive species are growing as new introductions are accelerating worldwide and show no signs of slowing. The study and management of invasive species is primarily oriented toward preventing further spread and successfully controlling or eradicating existing invasive populations. This drives a need for geographic approaches to detection, mapping, and modeling that describe species distributions and impacts, and contribute to better understanding the drivers and pathways that influence spread. Emerging techniques range from DNA sequencing to satellite remote sensing, static environmental models to dynamic forecasts, and rely on knowledge from domains as diverse as ecology, epidemiology, geography, and sociology. These interdisciplinary approaches are opening the door for near real‐time geospatial decision analytics tools and insights necessary for understanding and managing the significant and growing threat invasive species present to human wellbeing and the environment.