Global mean surface air temperature has risen since pre-industrial times and is expected to increase further in the future due to anthropogenic emissions of greenhouse gases. Global warming and associated changes in climate and environment at global and regional scales have been received increasing attention in recent decades. The extent of global mean temperature increase in the 21st century is of great scientific and socio-economic interest. A central issue for scientific research is the value of equilibrium climate sensitivitythe equilibrium change in global mean 2-m air temperature that would result from a sustained doubling of the atmospheric carbon dioxide concentration. Following the discussion of equilibrium climate sensitivity published in the anniversary issue of Science in 2005, here we interpret this indicator with new insights from the scientific literature. In brief, the equilibrium climate sensitivity was suggested as being 1.5-4.5°C, on the basis of the earliest generation of atmosphere-slab ocean general circulation models in the late 1970s. These values were confirmed by a hierarchy of climate models ranging from atmosphere-slab ocean to atmosphere-ocean general circulation models in the 1990s and the early 2000s and were used in the Intergovernmental Panel on Climate Change (IPCC) First to Third Assessment Reports. That range was reduced to 2.0-4.5°C by the IPCC Fourth Assessment Report in 2007, but was estimated at 1.5-4.5°C again by state of the art climate and Earth system models in the IPCC Fifth Assessment Report in 2013. Much effort is needed to improve our understanding of clouds and aerosolsthe biggest sources of uncertaintyin the real world and then in climate and Earth system models. Due to limitations concerning instrument records prior to the last century, attention should also be given to changes in climate during the distant past, either through the use of reconstructions or simulations, in order to reduce uncertainties in equilibrium climate sensitivity.