Horse breeders are interested in how traits will be transmitted to offspring. The basic rules of inheritance are the same for all genes. Every horse gets a complete genome from both the sire and the dam. While the rules of inheritance are the same for all genes, the way that genes determine traits is different for different traits.

Any given trait has an attribute called heritability. This is an indication of the extent to which genetics determines the trait. In humans, the language that you speak is not heritable. If a baby from China grows up in France, the baby will speak French, not Chinese. Language is a trait that is entirely dependent on environment. At the other extreme, some traits are entirely determined by genetics, often by single genes. In horses, genes affecting coat color are of this type, and coat color is said to have a very high heritability.

Many traits of importance to horse breeders are complex traits, affected by multiple genetic and environmental factors. Performance and conformation are both affected by a number of genes, many with small effects. Performance is also strongly affected by environment (training).

Gregor Mendel, a Moravian friar working with pea plants, worked out the basic rules of inheritance in the 19th century. He picked traits that were highly heritable. Single genes determined all of the traits, and hybrids between two true-breeding lines always exactly resembled one parent. The different forms of the genes that he worked with are called different alleles. In hybrids, one of the alleles (the one determining the trait that was seen) was called dominant, while the other allele (the one determining the trait that would reappear in subsequent generations) was called recessive. Mendel showed that during sexual reproduction, each parent contributed one of its two alleles to each gamete. Union of gametes during fertilization is random, so it is possible to predict the frequency of different types of offspring using simple rules of probability.