Abstract. Angiosperm leaves manifest a remarkable diversity of shapes that range from developmental sequences within a shoot and within crown response to microenvironment to variation among species within and between communities and among orders or families. It is generally assumed that because photosynthetic leaves are critical to plant growth and survival, variation in their shape reflects natural selection operating on function. Several non-mutually exclusive theories have been proposed to explain leaf shape diversity. These include: thermoregulation of leaves especially in arid and hot environments, hydraulic constraints, patterns of leaf expansion in deciduous species, biomechanical constraints, adaptations to avoid herbivory, adaptations to optimise light interception and even that leaf shape variation is a response to selection on flower form. However, the relative importance, or likelihood, of each of these factors is unclear. Here we review the evolutionary context of leaf shape diversification, discuss the proximal mechanisms that generate the diversity in extant systems, and consider the evidence for each the above hypotheses in the context of the functional significance of leaf shape. The synthesis of these broad ranging areas helps to identify points of conceptual convergence for ongoing discussion and integrated directions for future research.