Tropical forests and coral reefs host a disproportionately large share of global biodiversity and provide ecosystem functions and services used by millions of people. Yet, ongoing climate change is leading to an increase in frequency and magnitude of extreme climatic events in the tropics, which, in combination with other local human disturbances, is leading to unprecedented negative ecological consequences for tropical forests and coral reefs. Here, we provide an overview of how and where climate extremes are affecting the most biodiverse ecosystems on Earth and summarize how interactions between global, regional and local stressors are affecting tropical forest and coral reef systems through impacts on biodiversity and ecosystem resilience. We also discuss some key challenges and opportunities to promote mitigation and adaptation to a changing climate at local and global scales. This article is part of the theme issue 'Climate change and ecosystems: threats, opportunities and solutions'.