Breeding of crop plants to make them more adapted to human agricultural systems has been on-going during domestication the last 10 000 years. However, only recently with the invention of the Mendelian principles of genetics and the subsequent development of quantitative genetics during the twentieth century has such genetic crop improvement become based on a general theory. During the last 50 years plant breeding has entered a molecular era based on molecular tools to analyse DNA, RNA and proteins and associate such molecular results with plant phenotype. These marker trait associations develop fast to enable more efficient breeding. However, they still leave a major part of breeding to be performed through selection of phenotypes using quantitative genetic tools. The ten chapters of this book illustrate this development.