An emerging idea in evolutionary biology is that inheritance implies more than the sole transmission of the DNA sequence across generations. Non-genetic inheritance of information across generations results from various processes that contribute to parent extendash offspring resemblance, a property that is called heritability.The concept of heritability has been generalized into that of inclusive heritability, which is the heredity of differences, including all forms of inheritance. It unifies genetic and non-genetic heritability into a single framework encompassing the multiple dimensions of inheritance. We briefly provide evidence for the four identified processes of non-genetic inheritance.Epigenetic changes in DNA expression result in epigenetic inheritance when they are transmitted across generations, thus contributing to the transgenerational transmission of phenotypic variation. Epigenetic changes are usually mediated by changes in environmental conditions. Examples include the inheritance of maternal behaviour in rodents or the inheritance of flower symmetry.Parental non-genetic effects can result in the inheritance of non-genetic information across generations, thus contributing to the non-genetic component of inclusive heritability. Examples include the inheritance of immunocompetence against given parasites in birds or flexible adaptation to the maternal light environment in plants.Ecological inheritance occurs when offspring inherit the habitat of their parents. This indicates that any modification of the environment that results from ancestral activity and that affects fitness will change subsequent selective pressures. Examples include the webs, nests, dams and burrows that numerous animal species create, but also the changes in atmospheric gases and soil nutrients brought about by bacteria and plant species.Culture is the part of phenotypic variance that is transmitted through social learning. Recent evidence suggests that cultural transmission is widespread among animals. Examples concern mate choice and species recognition. Cultural selection constitutes another engine of evolution when it interacts with natural selection in both animals and humans.Non-genetic inheritance can easily be confounded with genetic inheritance. It is the intricate network of genetic and non-genetic inheritance systems that produce parent extendash offspring resemblance, which constitutes the whole evolutionary potential of a trait quantified by inclusive heritability.We formally partition inclusive heritability and propose methods to disentangle its components in order to better integrate them into a comprehensive view of inheritance. We propose specific designs coupling field or experimental longitudinal data with animal model types of statistical tools.Such methods should help to unravel fascinating enigmas in evolution and medicine, such as major evolutionary transitions or the ‘missing heritability’ in the human genome.The time is ripe to broaden concepts of inheritance and heritability in order to fully grasp the richness of evolutionary processes, and we call for a multidimensional modern synthesis that would merge the current modern synthesis with an inclusive view of inheritance.