The aim of this paper is to define and explain the classical concepts of animal breeding value. The breeding value of animals for a trait represents the average additive effect of a gene transmitted from parents to offspring, as an individual trait for a trait. Throughout the past, various methods have been used to assess breeding values using the knowledge then available. With the development of technology and the discovery of new methods to obtain data that were not available until then, scientists have improved the methods so that they can discover the most accurate data in the assessment of breeding values. Further, the additive breeding value, the additive effect of genes, the concept of genetic variation, explain the types of genomic data, the ways in which they are estimated and used in the assessment of breeding values of animals. In this paper, the aim is also to present and explain the BLUP method, to describe the possibility of using genomic data that are important in assessing the breeding values of animals. The research of genomic data has led to progress and unsurpassed BLUP method in GBLUP method which proved to be successful and better for further research and improvement in the field of selection. Genomic selection is based on breeding value that is directly assessed from one or part of the genome using genetic markers. Genomic selection leads to more data and better use of data on various traits. The emphasis is on the systematization of all methods used in gBLUP, and a review of previous achievements and discoveries in quantitative genetics.