Evolutionary biology traditionally equates inheritance with transmission of genes from parents to offspring. However, recent literature calls for considering ‘non-genetic inheritance’ in evolutionary theory. These calls have met with substantial scepticism. What is more, they appear to have caused further confusion both with respect to what inheritance is and what types of inheritance mechanisms are evolutionarily consequential. Building on previous work, we make use of the Price Equation to outline a general discussion of how non-genetic inheritance can affect phenotypic change within populations, exemplified by epigenetic inheritance. This shows that integrating non-genetic inheritance in evolutionary theory will require specific attention to the developmental processes that shape the relationship between the fitness of parents and the phenotype of their offspring.