The angiosperm flower develops through a modular programme which, although ancient and conserved, provides the flexibility that has allowed an almost infinite variety of floral forms to emerge. In this review, we explore the evolution of floral diversity, focusing on our recent understanding of the mechanistic basis of evolutionary change. We discuss the various ways in which flower size and floral organ size can be modified, the means by which flower shape and symmetry can change, and the ways in which floral organ position can be varied. We conclude that many challenges remain before we fully understand the ecological and molecular processes that facilitate the diversification of flower structure.