Ageing, and particularly the onset of age-related diseases, is associated with tissue dysfunction and macromolecular damage, some of which can be attributed to accumulation of oxidative damage. Polyphenolic natural products such as stilbenoids, flavonoids and chalcones have been shown to be effective at ameliorating several age-related phenotypes, including oxidative stress, inflammation, impaired proteostasis and cellular senescence, both in vitro and in vivo. Here we aim to identify the structural basis underlying the pharmacology of polyphenols towards ROS and related biochemical pathways involved in age-related disease. We compile and describe SAR trends across different polyphenol chemotypes including stilbenoids, flavonoids and chalcones, review their different molecular targets and indications, and identify common structural ground between chemotypes and mechanisms of action. In particular, we focus on the structural requirements for the direct scavenging of reactive oxygen/nitrogen species such as radicals as well as coordination of a broader antioxidant response. We further suggest that it is important to consider multiple (rather than single) biological activities when identifying and developing new medicinal chemistry entities with utility in modulating complex biological properties such as cell ageing.