Current knowledge of the genetic, epigenetic, behavioural and symbolic systems of inheritance requires a revision and extension of the mid-twentieth-century, gene-based, 'Modern Synthesis' version of Darwinian evolutionary theory. We present the case for this by first outlining the history that led to the neo-Darwinian view of evolution. In the second section we describe and compare different types of inheritance, and in the third discuss the implications of a broad view of heredity for various aspects of evolutionary theory. We end with an examination of the philosophical and conceptual ramifications of evolutionary thinking that incorporates multiple inheritance systems.