Plant breeding is the science of maximizing positive genetic traits in plants that people grow. It consists of analytical frameworks that allow researchers to create and select plants that are consistently outstanding in desired traits. The central objective in plant breeding is to improve the genetic basis of commercial crop species to comply with changing demands on yield and quality. Statistics plays a key role in modern plant breeding. A classical quantitative genetic model writes the phenotype as an outcome of genetic, environmental and genotype by environment interaction effects. In the genomic era, this classical model has been extended and generalized. Linear mixed models played an important role in classical quantitative genetics and still do so in modern.