Global climate change is a major threat to biodiversity. The most common methods for predicting the response of biodiversity to changing climate do not explicitly incorporate fundamental evolutionary and ecological processes that determine species responses to changing climate, such as reproduction, dispersal, and adaptation. We provide an overview of an emerging mechanistic spatial theory of species range shifts under climate change. This theoretical framework explicitly defines the ecological processes that contribute to species range shifts via biologically meaningful dispersal, reproductive, and climate envelope parameters. We present methods for estimating the parameters of the model with widely available species occurrence and abundance data and then apply these methods to empirical data for 12 North American butterfly species to illustrate the potential use of the theory for global change biology. The model predicts species persistence in light of current climate change and habitat loss. On average, we estimate that the climate envelopes of our study species are shifting north at a rate of 3.25 +/- 1.36 km/yr (mean +/- SD) and that our study species produce 3.46 +/- 1.39 (mean +/- SD) viable offspring per individual per year. Based on our parameter estimates, we are able to predict the relative risk of our 12 study species for lagging behind changing climate. This theoretical framework improves predictions of global change outcomes by facilitating the development and testing of hypotheses, providing mechanistic predictions of current and future range dynamics, and encouraging the adaptive integration of theory and data. The theory is ripe for future developments such as the incorporation of biotic interactions and evolution of adaptations to novel climatic conditions, and it has the potential to be a catalyst for the development of more effective conservation strategies to mitigate losses of biodiversity from global climate change.