Risk assessments of invasive species present one of the most challenging applications of species distribution models (SDMs) due to the fundamental issues of distributional disequilibrium, niche changes, and truncation. Invasive species often occupy only a fraction of their potential environmental and geographic ranges, as their spatiotemporal dynamics are shaped by intraspecific variability, human-mediated introductions, novel biotic interactions, climate change, rapid selection, and ecological niche shifts. Traditional correlative SDMs struggle to capture these processes because they implicitly assume distributions are at equilibrium and rely on observed occurrences that seldom represent the full environmental niche of invasive species. Predicting future potential distributions therefore requires moving beyond simple climate-matching approaches to models that explicitly capture the mechanisms underlying species responses to their environment. Mechanistic Niche Models (MNMs) are process-explicit models that address these limitations by capturing species' performance across environmental gradients. By incorporating physiological constraints and vital rates, MNMs offer a mechanistic understanding of species-environment relationships and enable more robust predictions onto novel environments. However, a unified MNM framework remains elusive. In this review, we delve into the theoretical foundations of MNMs, emphasizing their advantages over correlative approaches, focusing on invasive species. We provide insights into diverse modelling techniques across taxa and examine the benefits and limitations of MNMs for predicting species distributions under novel conditions. Our systematic review reveals that MNMs have been applied sparingly to invasive species, focusing primarily on insects and plants, likely due to high data requirements. MNMs constitute the most suitable approach for defining species distribution limits under novel conditions, but their success depends on the relevance of input data and effective parameterisation, including genotype selection, model type, experimental conditions, and physiological curve-fitting techniques. MNMs offer significant potential for advancing ecological research and providing robust tools for evidence-based management decisions for populations in disequilibrium under changing environmental conditions.