<p>Empirical evidence shows that evolution may take place during species’ range expansion. Indeed, dispersal ability tends to be selected for at the leading edge of invasions, ultimately increasing a species’ spreading speed. However, for organisms across many different taxa, higher dispersal comes at the cost of fitness, producing evolutionary trade-offs at the leading edge. Using reaction-diffusion equations and adaptive dynamics, we provide new insights on how such evolutionary processes take place. We show how evolution may drive phenotypes at the leading edge to maximize the asymptotic spreading speed, and we give conditions under which phenotypic plasticity in dispersal is selected for under different dispersal-reproduction trade-off scenarios. We provide some possible future research directions and other systems where the framework can be applied.</p>