Evolutionary biologists studying wild species have demonstrated that genetic and non-genetic sources of information are inherited across generations and are therefore responsible for phenotypic resemblance between relatives. Although it has been postulated that non-genetic sources of inheritance are important in natural selection, they are not taken into account for livestock selection that is based on genetic inheritance only. According to the natural selection theory, the contribution of non-genetic inheritance may be significant for the transmission of characters. If this theory is confirmed in livestock, not considering non-genetic means of transmission in selection schemes might prevent achieving maximum progress in the livestock populations being selected. The present discussion paper reviews the different mechanisms of genetic and non-genetic inheritance reported in the literature as occurring in livestock species. Non-genetic sources of inheritance comprise information transmitted via physical means, such as epigenetic and microbiota inheritance, and those transmitted via learning mechanisms: behavioral, cultural and ecological inheritance. In the first part of this paper we review the evidence that suggests that both genetic and non-genetic information contribute to inheritance in livestock (i.e. transmitted from one generation to the next and causing phenotypic differences between individuals) and discuss how the environment may influence non-genetic inherited factors. Then, in a second step, we consider methods for favoring the transmission of non-genetic inherited factors by estimating and selecting animals on their extended transmissible value and/or introducing favorable non-genetic factors via the animals' environment.