Advances in plant cell molecular biology have considerably increased our understanding of pollen-pistil barriers, particularly those operated by incompatibility mechanisms, and, at the same time, demonstrated the complexity and diversity of rejection systems once considered to be relatively simple. This book reviews the impressive knowledge acquired in the last century on the biology, particularly the inheritance and population genetics of self-incompatibility, and presents the new approaches to the study of the structure, function and evolution of incompatibility alleles and the analysis of cell-cell recognition and pollen rejection. The different methods now available for transforming the breeding behaviour of higher plants are also discussed.