The projected large increases in damaging ultraviolet radiation as a result of global emissions of ozone-depleting substances have been forestalled by the success of the Montreal Protocol. New challenges are now arising in relation to climate change. We highlight the complex interactions between the drivers of climate change and those of stratospheric ozone depletion, and the positive and negative feedbacks among climate, ozone and ultraviolet radiation. These will result in both risks and benefits of exposure to ultraviolet radiation for the environment and human welfare. This Review synthesizes these new insights and their relevance in a world where changes in climate as well as in stratospheric ozone are altering exposure to ultraviolet radiation with largely unknown consequences for the biosphere.