AbstractUnderstanding the movement of species’ ranges is a classic ecological problem that takes on urgency in this era of global change. Historically treated as a purely ecological process, range expansion is now understood to involve eco‐evolutionary feedbacks due to spatial genetic structure that emerges as populations spread. We synthesize empirical and theoretical work on the eco‐evolutionary dynamics of range expansion, with emphasis on bridging directional, deterministic processes that favor evolved increases in dispersal and demographic traits with stochastic processes that lead to the random fixation of alleles and traits. We develop a framework for understanding the joint influence of these processes in changing the mean and variance of expansion speed and its underlying traits. Our synthesis of recent laboratory experiments supports the consistent role of evolution in accelerating expansion speed on average, and highlights unexpected diversity in how evolution can influence variability in speed: results not well predicted by current theory. We discuss and evaluate support for three classes of modifiers of eco‐evolutionary range dynamics (landscape context, trait genetics, and biotic interactions), identify emerging themes, and suggest new directions for future work in a field that stands to increase in relevance as populations move in response to global change.