Ozone is the third most important anthropogenic greenhouse gas after carbon dioxide and methane but has a larger uncertainty in its radiative forcing, in part because of uncertainty in the source characteristics of ozone precursors, nitrogen oxides, and volatile organic carbon that directly affect ozone formation chemistry. Tropospheric ozone also negatively affects human and ecosystem health. Biomass burning (BB) and urban emissions are significant but uncertain sources of ozone precursors. Here, we report global-scale, in situ airborne measurements of ozone and precursor source tracers from the NASA Atmospheric Tomography mission. Measurements from the remote troposphere showed that tropospheric ozone is regularly enhanced above background in polluted air masses in all regions of the globe. Ozone enhancements in air with high BB and urban emission tracers (2.1 to 23.8 ppbv [parts per billion by volume]) were generally similar to those in BB-influenced air (2.2 to 21.0 ppbv) but larger than those in urban-influenced air (-7.7 to 6.9 ppbv). Ozone attributed to BB was 2 to 10 times higher than that from urban sources in the Southern Hemisphere and the tropical Atlantic and roughly equal to that from urban sources in the Northern Hemisphere and the tropical Pacific. Three independent global chemical transport models systematically underpredict the observed influence of BB on tropospheric ozone. Potential reasons include uncertainties in modeled BB injection heights and emission inventories, export efficiency of BB emissions to the free troposphere, and chemical mechanisms of ozone production in smoke. Accurately accounting for intermittent but large and widespread BB emissions is required to understand the global tropospheric ozone burden.