Earth's forests harbor extensive biodiversity and are currently a major carbon sink. Forest conservation and restoration can help mitigate climate change; however, climate change could fundamentally imperil forests in many regions and undermine their ability to provide such mitigation. The extent of climate risks facing forests has not been synthesized globally nor have different approaches to quantifying forest climate risks been systematically compared. We combine outputs from multiple mechanistic and empirical approaches to modeling carbon, biodiversity, and disturbance risks to conduct a synthetic climate risk analysis for Earth's forests in the 21st century. Despite large uncertainty in most regions we find that some forests are consistently at higher risk, including southern boreal forests and those in western North America and parts of the Amazon.