Parents influence the development of their offspring in many ways beyond the transmission of DNA. This includes transfer of epigenetic states, nutrients, antibodies and hormones, and behavioural interactions after birth. While the evolutionary consequences of such non-genetic inheritance are increasingly well understood, less is known about how inheritance mechanisms evolve. Here, we present a simple but versatile model to explore the adaptive evolution of non-genetic inheritance. Our model is based on a switch mechanism that produces alternative phenotypes in response to different inputs, including genes and non-genetic factors transmitted from parents and the environment experienced during development. This framework shows how genetic and non-genetic inheritance mechanisms and environmental conditions can act as cues by carrying correlational information about future selective conditions. Differential use of these cues is manifested as different degrees of genetic, parental or environmental morph determination. We use this framework to evaluate the conditions favouring non-genetic inheritance, as opposed to genetic determination of phenotype or within-generation plasticity, by applying it to two putative examples of adaptive non-genetic inheritance: maternal effects on seed germination in plants and transgenerational phase shift in desert locusts. Our simulation models show how the adaptive value of non-genetic inheritance depends on its mechanism, the pace of environmental change, and life history characteristics.