The role of evolutionary theory at the origin of life is an extensively debated topic. The origin and early development of life is usually separated into a prebiotic phase and a protocellular phase, ultimately leading to the Last Universal Common Ancestor. Most likely, the Last Universal Common Ancestor was subject to Darwinian evolution, but the question remains to what extent Darwinian evolution applies to the prebiotic and protocellular phases. In this review, we reflect on the current status of evolutionary theory in origins of life research by bringing together philosophy of science, evolutionary biology, and empirical research in the origins field. We explore the various ways in which evolutionary theory has been extended beyond biology; we look at how these extensions apply to the prebiotic development of (proto)metabolism; and we investigate how the terminology from evolutionary theory is currently being employed in state-of-the-art origins of life research. In doing so, we identify some of the current obstacles to an evolutionary account of the origins of life, as well as open up new avenues of research.