Methods of genomic value prediction are reviewed. The majority of the methods are related to mixed model methodology, either explicitly or implicitly, by treating systematic environmental effects as fixed and quantitative trait locus (QTL) effects as random. Six different methods are reviewed, including least squares (LS), ridge regression, Bayesian shrinkage, least absolute shrinkage and selection operator (Lasso), empirical Bayes and partial least squares (PLS). The LS and PLS methods are non-Bayesian because they do not require probability distributions for the data. The PLS method is introduced as a special dimension reduction scheme to handle high-density marker information. Theory and methods of cross-validation are described. The leave-one-out cross-validation approach is recommended for model validation. A working example is used to demonstrate the utility of genome selection (GS) in barley. The data set contained 150 double haploid lines and 495 DNA markers covering the entire barley genome, with an average marker interval of 2·23 cM. Eight quantitative traits were included in the analysis. GS using the empirical Bayesian method showed high predictability of the markers for all eight traits with a mean accuracy of prediction of 0·70. With traditional marker-assisted selection (MAS), the average accuracy of prediction was 0·59, giving an average gain of GS over MAS of 0·11. This study provided strong evidence that GS using marker information alone can be an efficient tool for plant breeding.