Recent theories regarding the evolution of predator-prey interactions isreviewed. This includes theory about the dynamics and stability of bothpopulations and traits, as well as theory predicting how predatory andanti-predator traits should respond to environmental changes. Evolution canstabilize or destabilize interactions; stability is most likely when only thepredator evolves, or when traits in one or both species are under strongstabilizing selection. Stability seems least likely when there is coevolutionand a bi-directional axis of prey vulnerability. When population cycles exist,adaptation may either increase or decrease the amplitude of those cycles. Anincrease in the defensive ability of prey is less likely to produceevolutionary counter-measures in its partner than is a comparable increase inattack ability of the predator. Increased productivity may increase or decreaseoffensive and defensive adaptations. The apparent predominance of evolutionaryresponses of prey to predators over those of predators to prey is in generalaccord with equilibrium theory, but theory on stability may be difficult toconfirm or refute. Recent work on geographically structured populationspromises to advance our understanding of the evolution of predator-preyinteractions.