There is a growing interest in using trait-based approaches to characterize the functional structure of animal communities. Quantitative methods have been derived mostly for plant ecology, but it is now common to characterize the functional composition of various systems such as soils, coral reefs, pelagic food webs or terrestrial vertebrate communities. With the ever-increasing availability of distribution and trait data, a quantitative method to represent the different roles of animals in a community promise to find generalities that will facilitate cross-system comparisons. There is, however, currently no theory relating the functional composition of food webs to their dynamics and properties. The intuitive interpretation that more functional diversity leads to higher resource exploitation and better ecosystem functioning was brought from plant ecology and does not apply readily to food webs. Here we appraise whether there are interpretable metrics to describe the functional composition of food webs that could foster a better understanding of their structure and functioning. We first distinguish the various roles that traits have on food web topology, resource extraction (bottom-up effects), trophic regulation (top-down effects), and the ability to keep energy and materials within the community. We then discuss positive effects of functional trait diversity on food webs, such as niche construction and bottom-up effects. We follow with a discussion on the negative effects of functional diversity, such as enhanced competition (both exploitation and apparent) and top-down control. Our review reveals that most of our current understanding of the impact of functional trait diversity on food web properties and functioning comes from an over-simplistic representation of network structure with well-defined levels. We, therefore, conclude with propositions for new research avenues for both theoreticians and empiricists.