Quantitative genetic theories based on infinitesimal model have been very successful in selecting the best animals in the last century. One of the methods based on IFM that has been used widely in quantitative genetics is best linear unbiased prediction (BLUP). Despite, because of the limited amount of genetic material and finite number of loci for each trait some infinitesimal models assumptions can be violated. Since 1970, molecular genetics has opened this black box by mapping the single genes affecting the quantitative traits. Therefore in the past 15 years, the major effort in animal breeding has changed from quantitative to molecular genetics with emphasis on marker assisted SELECTION (MAS).However, results have been modest. In 2001, based on a computer simulation study, genomic SELECTION as markers covering the whole genome was proposed as a variant of MAS. Simulated and real results have been shown that the breeding values could be predicted with higher accuracy in genomic SELECTION than traditional SELECTION. According to expert assessments, genomic SELECTION makes it possible to save 92% of the funds spent on traditional SELECTION and it is twice as efficient as the latter. However, there is a long way for reaching to phenotype from genotype; nevertheless, new technologies such as genomics, transcriptomics, proteomics and metabolomics can be useful in this way.