Present-day ecosystems face a variety of threats, such as invasive species, whose effects permeate entire communities. Partly for this reason, community ecology has been quick to embrace more holistic approaches that consider all species within an ecosystem and the collection of interactions between them within a network formalism. Perhaps because it draws on tools from graph theory and statistical physics, a cornerstone idea in this network approach is the notion that ecological networks are paradigmatic complex systems. In this talk, I will argue that the majority of research during the past few decades actually demonstrates that the exact opposite is true. To demonstrate this point, I will begin by outlining the growing body of network studies that describe ubiquitous structural patterns that link different ecological networks together, independent of details like where they come from or their particular species composition. I will then describe how adopting a more evolutionary perspective---built by the incorporation of species' phylogenetic relatedness or macro-evolutionary models into network studies---has provided evidence to support the mechanisms that underpin these structual patterns. Finally, I will conclude by explaining how the apparent "limits" to ecological complexity are not a drawback but instead direct us to an exciting new set of open research questions.