The hydroxyl radical, OH, initiates the removal of the majority of trace gases in the atmosphere, and together with the closely coupled species, the hydroperoxy radical, HO₂, is intimately involved in the oxidation chemistry of the atmosphere. This critical review discusses field measurements of local concentrations of OH and HO₂ radicals in the troposphere, and in particular the comparisons that have been made with numerical model calculations containing a detailed chemical mechanism. The level of agreement between field measurements of OH and HO₂ concentrations and model calculations for a given location provides an indication of the degree of understanding of the underlying oxidation chemistry. We review the measurement-model comparisons for a range of different environments sampled from the ground and from aircraft, including the marine boundary layer, continental low-NO_x regions influenced by biogenic emissions, the polluted urban boundary layer, and polar regions. Although good agreement is found for some environments, there are significant discrepancies which remain unexplained, a notable example being unpolluted, forested regions. OH and HO₂ radicals are difficult species to measure in the troposphere, and we also review changes in detection methodology, quality assurance procedures such as instrument intercomparisons, and potential interferences.