Over the past decade, satellite-based measurements of column-averaged carbon dioxide concentration, called XCO2, have proliferated with sensors such as GOSAT, OCO-2, and TanSAT.  Even more capable systems are planned to be launch in the future into both polar and geostationary orbits, in the hopes of using these measurements to answer fundamental questions about the carbon cycle and to possibly measure or even monitor anthropogenic emissions of CO2.  Previous work has shown that persistent spatiotemporal biases in satellite measurements of CO2 can lead to spurious flux signals, when these measurements are assimilated into inverse carbon flux models.   Biases of even 1 ppm (out of the ~400 ppm) are unacceptable, and must ideally be at most a few tenths of a ppm, or even less.  Such a tight measurement requirement represents a daunting challenge for both instruments and retrieval algorithms alike.

Retrieval algorithms for these types of measurements have continued to evolve, and generally use optimal-estimation type retrievals to solve for XCO2 as well as a host of other variables on which the radiances depend, such as surface reflectivity, cloud and aerosol scattering parameters, refinements to meteorological variables, and some instrument parameters.  In this talk we give a broad overview of different retrieval approaches, and discuss progress towards achieving the highest-accuracy measurements possible, specifically from the OCO-2 instrument.   We discuss particular issues that can lead to XCO2 biases, and ways to deal with them. It is found that while systematic errors have generally decreased over time because of improvements in spectroscopy, instrument characterization, and the retrieval itself, important systematic errors remain.  We discuss possible future improvements to further minimize these systematic errors, in order to help achieve our lofty goal of the accurate measurement of surface fluxes on local and regional scales.