Widespread use of transgenic crops that express an insecticidal endotoxin from Bacillus thuringiensis increases the risk of evolution of resistance by the European corn borer and other insect pests. To delay resistance evolution, the high-dose/refuge strategy is being implemented for Bt maize and Bt cotton. We develop a general modelling framework to understand the invasion and spread of alleles conferring resistance. We show that at least three processes are involved in explaining the effectiveness of the high-dose/refuge strategy: the intensity of selection, assortative (non-random) mating due to spatial subdivision, and variation in male mating success also due to spatial subdivision. Understanding these processes leads to a greater range of possible resistance management tactics. For example, efforts to encourage adults to leave their natal fields may have the unwanted effect of speeding rather than slowing resistance evolution. Furthermore, when Bt maize causes high mortality to susceptible target pests, spraying insecticides in refuges to reduce pest populations may not greatly disrupt resistance management.