Ecological networks are schematic representations of species’ interactions in an ecosystem. The study of these structures provides insights into the assembly of ecological communities (restoration) and their collapse (conservation) from the perspective of multiple trophic levels. Recent work has highlighted the role of species and groups of species that are 'key players' in these networks, providing measures of species’ importance and outlining management strategies for conservation ecologists.  Parallel research has concentrated on ecological succession, speciation models, and metapopulation models of ecological networks that can account for the assembly of ecological communities.  We review here recent contributions and define key concepts such as cascading extinctions, robustness and fragility of ecological networks.  While previous research has focused primarily on the role of  'key species' that maintain the network connected, we show instead how the relations between species can be crucial for network robustness and propose a proper 'taxonomy' of ecological connections.  We specifically introduce the notions of functional and redundant connections and show that in empirical food webs around 90% of the links are functional, playing a role in the robustness of the network.  This change of perspective will show that a species’ importance depends critically on the nature of its connections rather than simply on their number. Finally, main open problems and future directions will be outlined.