Natural ecosystems are complex assemblages composed of many species, interacting together both directly and indirectly, through their environment. The coupled population dynamics (growth, death and reproduction of species) and evolutionary dynamics (Darwinian natural selection acting on species attributes) in such systems can generate a wide range of behaviors. Ecology has long studied how ecosystem complexity should affect their stability and/or productivity, but evolutionary dynamics has received less attention. Using the mathematical framework of adaptive dynamics, we can study how ecological diversity impacts the evolutionary dynamics of ecosystems, and reciprocally, how evolutionary past can alter the diversity-functioning relationship in communities.