Although coevolution is complicated, in that the interacting species evolve in response to each other, such evolutionary dynamics are amenable to mathematical modeling. In this article, we briefly review models and data on coevolution between plants and the pathogens and herbivores that attack them. We focus on "arms races," in which trait values in the plant and its enemies escalate to more and more extreme values. Untested key assumptions in many of the models are the relationships between costs and benefits of resistance in the plant and the level of resistance, as well as how costs of virulence or detoxification ability in the enemy change with levels of these traits. A preliminary assessment of these assumptions finds only mixed support for the models. What is needed are models that are more closely tailored to particular plant-enemy interactions, as well as experiments that are expressly designed to test existing models.