Despite mounting calls for predictive ecological approaches rooted in physiological performance currencies, the field of invasive species biology has lagged behind. For instance, successful invaders are often predicted to consume diverse foods, but the nutritional complexity of foods often leaves food-level analyses short of physiological mechanisms. The emerging field of nutritional geometry (NG) provides new theory and empirical tools to predict invasive potential based on fundamental and realized nutritional niches. We review recent advances and synthesize NG predictions about behavioral traits that favor invasive establishment, and evolutionary dynamics that promote invasive spread. We also provide practical advice for applying NG approaches, and discuss the power of nutrition to achieve a more predictive invasion biology that explicitly integrates physiological mechanisms.