Angiosperms and their flowers have greatly diversified into an overwhelming array of forms in the past 135 million years. Diversification was shaped by changes in climate and the biological environment (vegetation, interaction with other organisms) and by internal structural constraints and potentials. This review focuses on the development and structural diversity of flowers and structural constraints. It traces floral diversification in the different organs and organ complexes (perianth, androecium, gynoecium) through the major clades of extant angiosperms. The continuously improved results of molecular phylogenetics provide the framework for this endeavor, which is necessary for the understanding of the biology of the angiosperms and their flowers. Diversification appears to work with innovations and modifications of form. Many structural innovations originated in several clades and in special cases could become key innovations, which likely were hot spots of diversification. Synorganization between organs was an important process to reach new structural levels, from which new diversifications originated. Complexity of synorganization reached peaks in Orchidaceae and Apocynaceae with the independent evolution of pollinaria. Such a review throughout the major clades of angiosperms also shows how superficial and fragmentary our knowledge on floral structure in many clades is. Fresh studies and a multidisciplinary approach are needed.