Climate change is driven primarily by anthropogenic emissions of greenhouse gases, chief among them carbon dioxide and methane. Two fundamental challenges in carbon cycle science are (1) to quantify human emissions of greenhouse gases at scales ranging from the individual to the globe and from hours to decades, and (2) to anticipate how the “natural” (e.g. oceans, land) components of the carbon cycle will act to mitigate or to amplify the impact of human emissions. Spatiotemporal variability in observations of atmospheric concentrations of greenhouse gases can be used to tackle both challenges, because the atmosphere preserves signatures of emissions and uptake (a.k.a. fluxes) of greenhouse gases at the Earth’s surface. The process is analogous to being handed a creamy cup of coffee and being asked to infer not only when and where the cream was originally added to the cup, but ideally also who poured it in and why. This talk will give an overview of the use of inverse problems in carbon cycle science, focusing on the question of whether we can use atmospheric observations not only to quantify and locate fluxes but also to directly probe the underlying biogeochemical processes and their sensitivity to climate change.