Abstract The leaves of extant terrestrial plants show highly diverse and elaborate patterns of leaf venation. One fundamental feature of many leaf venation patterns, especially in the case of angiosperm leaves, is the presence of anastomoses. Anastomosing veins distinguish a network topologically from a simple dendritic (tree-like) pattern which represents the primitive venation architecture. The high degree of interspecific variation of entire venation patterns as well as phenotypic plasticity of some venation properties, such as venation density, indicate the high selective pressure acting on this branching system. Few investigations deal with functional properties of the leaf venation system. The interrelationships between topological or geometric properties of the various leaf venation patterns and functional aspects are far from being well understood. In this review we summarize current knowledge of interrelationships between the form and function of leaf venation and the evolution of leaf venation patterns. Since the functional aspects of architectural features of different leaf venation patterns are considered, the review also refers to the topic of individual and intraspecific variation. One basic function of leaf venation is represented by its contribution to the mechanical behaviour of a leaf. Venation geometry and density influences mechanical stability and may affect, for example, susceptibility to herbivory. Transport of water and carbohydrates is the other basic function of this system and the transport properties are also influenced by the venation architecture. These various functional aspects can be interpreted in an ecophysiological context.