Permafrost temperatures have increased in polar and high-elevation regions, affecting the climate system and the integrity of natural and built environments. In this Review, we outline changes in the thermal state of permafrost, focusing on permafrost temperatures and active-layer thickness. Increases in permafrost temperature vary spatially owing to interactions between climate, vegetation, snow cover, organic-layer thickness and ground ice content. In warmer permafrost (temperatures close to 0 °C), rates of warming are typically less than 0.3 °C per decade, as observed in sub-Arctic regions. In colder permafrost (temperatures less than -2 °C), by contrast, warming of up to about 1 °C per decade is apparent, as in the high-latitude Arctic. Increased active-layer thicknesses have also been observed since the 1990s in some regions, including a change of 0.4 m in the Russian Arctic. Simulations unanimously indicate that warming and thawing of permafrost will continue in response to climate change and potentially accelerate, but there is substantial variation in the magnitude and timing of predicted changes between different models and scenarios. A greater understanding of longer-term interactions between permafrost, climate, vegetation and snow cover, as well as improved model representation of subsurface conditions including ground ice, will further reduce uncertainty regarding the thermal state of permafrost and its future response.