In this study, we show using a state-of-the-art Earth system model, UKESM1, that emissions and climate scenario depending, there could be large changes in surface ozone by the end of the twenty-first century, with unprecedentedly large increases over South and East Asia. We also show that statistical modelling of the trends in future ozone works well in reproducing the model output between 1900 and 2050. However, beyond 2050, and especially under large climate change scenarios, the statistical model results are in poorer agreement with the fully interactive Earth system model output. This suggests that additional processes occurring in the Earth system model such as changes in the production of ozone at higher temperatures or changes in the influx of ozone from the stratosphere, which are not captured by the statistical model, have a first order impact on the evolution of surface ozone over the twenty-first century. We show in a series of idealized box model simulations, with two different chemical schemes, that changes in temperature lead to diverging responses between the schemes. This points at the chemical mechanisms as being a source of uncertainty in the response of ozone to changes in temperature, and so climate, in the future. This underscores the need for more work to be performed to better understand the response of ozone to changes in temperature and constrain how well this relationship is simulated in models. This article is part of a discussion meeting issue 'Air quality, past present and future'.