Past management of exploited species and of conservation issues has often ignored the evolutionary dynamics of species. During the 70s and 80s, evolution was mostly considered a slow process that may be safely ignored for most management issues. However, in recent years, examples of fast evolution have accumulated, suggesting that time scales of evolutionary dynamics (variations in genotype frequencies) and of ecological dynamics (variations in species densities) are often largely comparable, so that complex feedbacks commonly exist between the ecological and the evolutionary context (``eco-evolutionary dynamics''). While a first approach is of course to consider the evolution of a given species, in ecological communities, species are interlinked by interaction networks. In the present article, I discuss how species (co)evolution in such a network context may alter our understanding and predictions for species coexistence, given the disturbed world we live in. I review some concepts and examples suggesting that evolution may enhance the robustness of ecological networks and then show that, in many situations, the reverse may also happen, as evolutionary dynamics can harm diversity maintenance in various ways. I particularly focus on how evolution modifies indirect effects in ecological networks, then move to coevolution and discuss how the outcome of coevolution for species coexistence depends on the type of interaction (mutualistic or antagonistic) that is considered. I also review examples of phenotypes that are known to be important for ecological networks and shown to vary rapidly given global changes. Given all these components, evolution produces indirect eco-evolutionary effects within networks that will ultimately influence the optimal management of the current biodiversity crisis.