Anticipation is the act of using information about the past and present to make predictions about future scenarios. As a concept, it is predominantly associated with the psychology of the human mind; however, there is accumulating evidence that diverse taxa without complex neural systems, and even biochemical networks themselves, can respond to perceived future conditions. Although anticipatory processes, such as circadian rhythms, stress priming, and cephalic responses, have been extensively studied over the last three centuries, newer research on anticipatory genetic networks in microbial species shows that anticipatory processes are widespread, evolutionarily old, and not simply reserved for neurological complex organisms. Overall, data suggest that anticipatory responses represent a unique type of biological processes that can be distinguished based on their organizational properties and mechanisms. Unfortunately, an empirically based biologically explicit framework for describing anticipatory processes does not currently exist. This review attempts to fill this void by discussing the existing examples of anticipatory processes in non-cognitive organisms, providing potential criteria for defining anticipatory processes, as well as their putative mechanisms, and drawing attention to the often-overlooked role of anticipation in the evolution of physiological systems. Ultimately, a case is made for incorporating an anticipatory framework into the existing physiological paradigm to advance our understanding of complex biological processes.