The social cost of carbon is the marginal impact of climate change. Estimates of the total impact of climate change show that a century of climate change is about as bad as losing a decade of economic growth. Poorer countries are more vulnerable. The uncertainties are vast and skewed the wrong way. The many published estimates of the social cost of carbon span six orders of magnitude, and some studies find support for a carbon subsidy. There is mixed evidence for publication bias. MATLAB code is used to illustrate key sensitivities of the social cost of carbon; readers can readily run their own analyses. The bulk of the published estimates suggests that carbon dioxide should be taxed somewhere between $20/tC and $400/tC, depending on the preferred rates of discount and risk aversion. Revealed preferences on carbon pricing are at the lower end of this range. The social cost of carbon rises at around 2% per year. The central estimate of the social cost of carbon has not moved much over the last two decades, but the range of estimates is tightening slowly.