Transport networks in biology have traditionally been considered to be branching trees, since such networks are thought to be optimal for transport. Yet, there are many natural examples, such as the foraging slime mold physarum polycephalum and the vasculature of the mammalian neocortex that exhibit dense sets of nested loops. The most ubiquitous of those examples is the modern leaf vasculature, a pervasive example of a complex biological transport network that is necessary for the survival of land plants and thought to be under strong evolutionary pressure. Leaf venation evolved from simple dichotomously branching structures to the modern densely reticulate architecture that we see today. We discuss how leaves evolved to their current form and consider possible reasons for the emergence of loops in biological transport networks. Inspired by their complex form, we use tools from statistical physics and computational topology to discuss the mathematics behind the reticulate topology, and what leaves can teach us about natural and man-made networks in general.