Given the unprecedented rate of species extinctions facing the planet, understanding the causes and consequences of species diversity in ecosystems is of paramount importance. Ecologists have investigated both the influence of environmental variables on species diversity and the influence of species diversity on ecosystem function and stability. These investigations have largely been carried out without taking into account the overarching stabilizing structures of food webs that arise from evolutionary and successional processes and that are maintained through species interactions. Here, we argue that the same large-scale structures that have been purported to convey stability to food webs can also help to understand both the distribution of species diversity in nature and the relationship between species diversity and food web stability. Specifically, the allocation of species diversity to slow energy channels within food webs results in the skewed distribution of interactions strengths that has been shown to confer stability to complex food webs. We end by discussing the processes that might generate and maintain the structured, stable and diverse food webs observed in nature.