Part of a collection: Classics in Biological Theory Leigh Van Valen was an American evolutionary biologist who made major contributions to evolutionary theory. He is particularly remembered for his groundbreaking paper “A New Evolutionary Law” (1973) where he provided evidence from fossil record data that the probability of extinction within any group remains essentially constant through time. In order to explain such an unexpected result, Van Valen formulated a very influential idea that he dubbed the “Red Queen hypothesis.” It states that the constant decay must be a consequence of evolutionary interactions among connected species within ecological networks. In Van Valen’s picture, species do not merely evolve: they also coevolve with other species. As a consequence, when thinking about adaptation to an external environment, the other species must be considered as part (maybe a major part) of such an external world. Van Valen’s law provided the first complex systems theory of coevolutionary dynamics and inspired a whole range of theoretical and experimental developments from very diverse fields, percolating far beyond its original formulation. Red Queen arms races are nowadays considered a widespread feature of complex adaptive systems. This work has been funded by the Botín Foundation and by the Santa Fe Institute.