Climate change will affect psychological wellbeing. Substantial research has documented harmful impacts on physical health, mental health, and social relations from exposure to extreme weather events that are associated with climate change. Recently, attention has turned to the possible effects of climate change on mental health through emotional responses such as increased anxiety. This paper discusses the nature of climate anxiety and some evidence for its existence, and speculates about ways to address it. Although climate anxiety appears to be a real phenomenon that deserves clinical attention, it is important to distinguish between adaptive and maladaptive levels of anxiety. A focus on individual mental health should not distract attention from the societal response that is necessary to address climate change.