In these times of rapidly changing climate, the science of detecting and modeling shifts in the ranges of tree species is advancing of necessity. We briefly review the current state of the science on several fronts. First, we review current and historical evidence for shifting ranges and migration. Next, we review two broad categories of methods, focused on the spatial domain, for modeling potential range shifts and future suitable habitat: empirical species-distribution models and more process-based simulations. We propose long-term demography studies as a complementary approach in the time domain when sufficient data are available. Dispersal and successful migration into newly suitable habitat are key mechanisms constraining range shifts. We review three approaches to estimating these processes, followed by a discussion of the potential for assisted migration. We conclude that there have been significant recent advances on several fronts but there are still large uncertainties that need further research.