'Reactive oxygen species' (ROS) is a generic term that defines a wide variety of oxidant molecules with vastly different properties and biological functions that range from signalling to causing cell damage. Consequently, the description of oxidants needs to be chemically precise to translate research on their biological effects into therapeutic benefit in redox medicine. This Expert Recommendation article pinpoints key issues associated with identifying the physiological roles of oxidants, focusing on H2O2 and O2.-. The generic term ROS should not be used to describe specific molecular agents. We also advocate for greater precision in measurement of H2O2, O2.- and other oxidants, along with more specific identification of their signalling targets. Future work should also consider inter-organellar communication and the interactions of redox-sensitive signalling targets within organs and whole organisms, including the contribution of environmental exposures. To achieve these goals, development of tools that enable site-specific and real-time detection and quantification of individual oxidants in cells and model organisms are needed. We also stress that physiological O2 levels should be maintained in cell culture to better mimic in vivo redox reactions associated with specific cell types. Use of precise definitions and analytical tools will help harmonize research among the many scientific disciplines working on the common goal of understanding redox biology.