Recent theories regarding the evolution of predator-prey interactions is re
viewed. This includes theory about the dynamics and stability of both popul
ations and traits, as well as theory predicting how predatory and anti-pred
ator traits should respond to environmental changes. Evolution can stabiliz
e or destabilize interactions; stability is most likely when only the preda
tor evolves, or when traits in one or both species are under strong stabili
zing selection. Stability seems least likely when there is coevolution and
a bi-directional axis of prey vulnerability. When population cycles exist,
adaptation may either increase or decrease the amplitude of those cycles. A
n increase in the defensive ability of prey is less likely to produce evolu
tionary countermeasures in its partner than is a comparable increase in att
ack ability of the predator. Increased productivity may increase or decreas
e offensive and defensive adaptations. The apparent predominance of evoluti
onary responses of prey to predators over those of predators to prey is in
general accord with equilibrium theory, but theory on stability may be diff
icult to confirm or refute. Recent work on geographically structured popula
tions promises to advance our understanding of the evolution of predator-pr
ey interactions.