Species often respond to human‐caused climate change by shifting where they occur on the landscape. To anticipate these shifts, we need to understand the forces that determine where species currently occur. We tested whether a long‐hypothesised trade‐off between climate and competitive constraints explains where tree species grow on mountain slopes. Using tree rings, we reconstructed growth sensitivity to climate and competition in range centre and range margin tree populations in three climatically distinct regions. We found that climate often constrains growth at environmentally harsh elevational range boundaries, and that climatic and competitive constraints trade‐off at large spatial scales. However, there was less evidence that competition consistently constrained growth at benign elevational range boundaries; thus, local‐scale climate‐competition trade‐offs were infrequent. Our work underscores the difficulty of predicting local‐scale range dynamics, but suggests that the constraints on tree performance at a large‐scale (e.g. latitudinal) may be predicted from ecological theory.