Genetic models convert data into estimated breeding values and other information useful to breeders. The goal is to provide accurate and timely predictions of the future performance for each animal (or embryo). Modeling involves defining traits, editing raw data, removing environmental effects, including genetic-by-environmental interactions and correlations among traits, and accounting for nonadditive inheritance or nonnormal distributions. Data included phenotypes and pedigrees during the last century and genotypes within the last decade. Genomic data can include markers, haplotypes, and causative effects such as insertions, deletions, or point mutations; most models also include polygenic effects because the markers do not track causative variants perfectly. Total numbers of known variants have increased rapidly from thousands to hundreds of thousands to millions. Nonlinear models add precision for traits influenced by major genes, but linear models work well for traits with more normally distributed genomic effects. Numbers of genotyped animals in US dairy evaluations increased rapidly from a few thousand in 2009 to about 1 million in 2015. Most are young females that will contribute to estimating allele effects in the future, but only about 100,000 have phenotypes so far. Traditional animal models may become biased by genomic preselection because Mendelian sampling of phenotyped progeny and mates is no longer expected to average 0. Single-step models that combine pedigree and genomic relationships can account for such selection, but approximations and new algorithms are needed to avoid excessive computation. Traditional animal models may include all breeds and crossbreds, but most genomic evaluations are still computed within breed. Inclusion of inbreeding, heterosis, dominance, and interactions can improve precision. Multitrait genomic models may be preferred for traits with many missing records or when foreign records are included as pseudo-observations, but most countries use multitrait traditional evaluations followed by single-trait genomic evaluations. A final goal is to explain how the models work so that breeders can more confidently apply the predictions in their selection programs.