The emergence of natural selection, requiring that reproducing entities present variations that may be inherited and passed on, was arguably the most important breakthrough in the self-organization of life. In this Perspective, the assumptions governing biological reproduction are confronted with physico-chemical principles that control the evolution of material systems. In biology, the reproduction of living organisms is never considered to be reversible, whereas microscopic reversibility is an essential principle in the physical description of matter. Here, we show that this discrepancy places constraints on the possibility of finding kinetic processes in the chemical world that are equivalent to natural selection in the biological one. Chemical replicators can behave in a similar fashion to living entities, provided that the reproduction cycle proceeds in a unidirectional way. For this to be the case, kinetic barriers must hinder the reverse process. The system must, thus, be held far from equilibrium and fed with a non-degraded (low-entropy) form of energy. The ensuing constraints must be factored in when proposing scenarios that account for the origin of life at the molecular level. The rules of biological reproduction and evolution may seem to, at first glance, conflict with simple physico-chemical principles. This Perspective identifies the constraints that must be placed on chemical processes in order for them to mimic natural selection seen in biology.