Equilibrium climate sensitivity characterizes the Earth' long-term global temperature response to an increased atmospheric carbon dioxide concentration. It has reached almost iconic status as the single number that describes how severe climate change will be. The consensus 'likely' range for climate sensitivity of 1.5-4.5 o C today is the same as given by Jule Charney in 1979, but is now based on quantitative evidence from across the climate system, and through climate history. The quest to constrain climate sensitivity has revealed important insights into the timescales of the climate system response, natural variability, limitations in observations and climate models, but also concerns about the simple concepts underlying climate sensitivity and radiative forcing, which open avenues to better understand and constrain the climate response to forcing. Estimates of the transient climate response are better constrained by observed warming and are more relevant for predicting warming over the next decades. Newer metrics relating global warming directly to the total emitted CO2 show that in order to keep warming to within 2 o C, future CO2 emissions have to remain strongly limited, irrespective of climate sensitivity being at the high or low end.If we increase the amount of CO2 in the Earth's atmosphere and wait for climate to respond, how much warmer would surface temperatures eventually get? What seems like a simple but important question to ask given current and projected human-induced CO2 emissions, is an issue that scientists have struggled with since the first rough estimates were made more than a century ago 1,2 . To answer that question, starting in the 1960s, scientists have used energy balance arguments combined with observed changes in the global energy budget, evaluated comprehensive climate models against observations, and analyzed the relationship between external forcing and climate change over different climate states in the past (see Methods for a list of early publications). The idea of using those different lines of evidence has not changed, but progress in simulating climate, a longer and more accurate observed record of past warming, and better constrained paleoclimate reconstructions now offer more possibilities to evaluate and constrain models. However, recent research has pointed out previously unknown limitations in some of the concepts and assumptions underlying a single constant climate sensitivity 3 . While publications have appeared using various methods, arguably the most important conceptual recent insights is that feedbacks change with equilibration time, an insight that is based on studies in comprehensive climate models. Other recent insights show that the treatment of observations is important 4 . Knowing, to first order, how the global climate will warm in response to increased CO2 is critical: for unabated emissions, it is the difference between a hot and an extremely hot future. The value of halving the uncertainty in that projection may be in the trillions of dollars 5 . Here w...