 We present the discussion of inheritance systems in the context of several debates. First, between proponents of monism about heredity (gene-centric views), holism about heredity (Developmental Systems Theory), and those stressing the role of multiple systems of inheritance. Second, between those analyzing inheritance solely in terms of replication and transmission, and views that stress the multi-generation reproduction of phenotypic traits. A third debate is concerned with different criteria that have been proposed for identifying and delimiting inheritance systems. A fourth controversy revolves around the evolutionary implications of the existence of the different inheritance systems, for example the significance of the “Lamarckian” aspects of some of the inheritance systems that have been identified, such as epigenetic inheritance and behavioral inheritance, as well as potentially the inheritance of microbial symbionts (i.e., the microbiome) that allow the transmission of environmentally induced characters (i.e., “soft inheritance”).