In its most recognizable form, coevolution is a natural process. It is ubiquitous in natural systems whether they are biological or social. But, a community of Evolutionary Computation researchers have also used computation and algorithms to artificially replicate coevolution. They do so for a rich variety of purposes. I will talk about the remarkable correspondences and contrasts between coevolution in nature and computation, and I will outline open challenges and opportunities in this fascinating, complex research area.