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Improving our understanding of species ranges under rapid climate change requires application of our knowledge of the tolerance and adaptive capacity of populations to changing environmental conditions. Here, we describe an emerging modelling approach, Delta TraitSDM, which attempts to achieve this by explaining species distribution ranges based on phenotypic plasticity and local adaptation of fitness-related traits measured across large geographical gradients. The collection of intraspecific trait data measured in common gardens spanning broad environmental clines has promoted the development of these new models - first in trees but now rapidly expanding to other organisms. We review, explain and harmonize the main findings from this new generation of models that, by including trait variation over geographical scales, are able to provide new insights into future species ranges. Overall, Delta TraitSDM predictions generally deliver a less alarming message than previous models of species distribution under new climates, indicating that phenotypic plasticity should help, to a considerable degree, some plant populations to persist under climate change. The development of Delta TraitSDMs offers a new perspective to analyse intraspecific variation in single and multiple traits, with the rationale that trait (co)variation and consequently fitness can significantly change across geographical gradients and new climates.