  Species do not merely evolve, they also coevolve with other organisms.
Coevolution is a major force driving interacting species to continuously evolve
ex- ploring their fitness landscapes. Coevolution involves the coupling of
species fit- ness landscapes, linking species genetic changes with their
inter-specific ecological interactions. Here we first introduce the Red Queen
hypothesis of evolution com- menting on some theoretical aspects and empirical
evidences. As an introduction to the fitness landscape concept, we review key
issues on evolution on simple and rugged fitness landscapes. Then we present
key modeling examples of coevolution on different fitness landscapes at
different scales, from RNA viruses to complex ecosystems and macroevolution.
