Genomic selection uses dense markers across the genome to estimate breeding values for quantitative traits. This paper discusses predicting breeding values using a linear combination of markers. The best estimate of each marker's effect is the expectation of its effect given the data. A prior distribution of marker effects is needed for this calculation. If marker effects are normally distributed, BLUP can be used to estimate marker effects and breeding values (EBVs). This model is equivalent to a conventional animal model where the relationship matrix is estimated from markers instead of pedigrees. The accuracy of EBVs can approach 1.0 but requires large data. An alternative model assumes only some markers have non-zero effects, following a reflected exponential distribution. This model has higher accuracy than the normal distribution model. Genomic selection may lead to a faster decline in selection response than phenotypic selection unless new markers are added. A method to maximize long-term selection response is derived, varying marker weights based on allele frequency. The classical model of quantitative traits assumes an infinite number of genes with small effects. Traditional selection is effective even with few genes. However, known genes have not greatly improved EBV-based selection. This is due to many genes affecting a trait, small effects, and limited knowledge of genes responsible for variation. Genomic selection uses dense markers to estimate all genetic variance. It has become feasible with advances in SNP technology. The paper discusses predicting breeding values from genomic data and an equivalent model using traditional mixed models. Long-term response depends on genetic details, while short-term response is predicted by the infinitesimal model. Genomic selection may lead to a faster decline in response than phenotypic selection. The paper derives the expected long-term response to genomic selection and shows how it can be maximized. The calculation of EBVs from genomic data involves estimating QTL genotypes from marker data. The true breeding value is the sum of QTL effects. EBVs are estimated using marker data, assuming regression coefficients are known. In practice, these coefficients must be estimated from data.Genomic selection uses dense markers across the genome to estimate breeding values for quantitative traits. This paper discusses predicting breeding values using a linear combination of markers. The best estimate of each marker's effect is the expectation of its effect given the data. A prior distribution of marker effects is needed for this calculation. If marker effects are normally distributed, BLUP can be used to estimate marker effects and breeding values (EBVs). This model is equivalent to a conventional animal model where the relationship matrix is estimated from markers instead of pedigrees. The accuracy of EBVs can approach 1.0 but requires large data. An alternative model assumes only some markers have non-zero effects, following a reflected exponential distribution. This model has higher accuracy than the normal distribution model. Genomic selection may lead to a faster decline in selection response than phenotypic selection unless new markers are added. A method to maximize long-term selection response is derived, varying marker weights based on allele frequency. The classical model of quantitative traits assumes an infinite number of genes with small effects. Traditional selection is effective even with few genes. However, known genes have not greatly improved EBV-based selection. This is due to many genes affecting a trait, small effects, and limited knowledge of genes responsible for variation. Genomic selection uses dense markers to estimate all genetic variance. It has become feasible with advances in SNP technology. The paper discusses predicting breeding values from genomic data and an equivalent model using traditional mixed models. Long-term response depends on genetic details, while short-term response is predicted by the infinitesimal model. Genomic selection may lead to a faster decline in response than phenotypic selection. The paper derives the expected long-term response to genomic selection and shows how it can be maximized. The calculation of EBVs from genomic data involves estimating QTL genotypes from marker data. The true breeding value is the sum of QTL effects. EBVs are estimated using marker data, assuming regression coefficients are known. In practice, these coefficients must be estimated from data.