Satellite measurements of greenhouse gases provide an important tool to monitor and inform emission reduction efforts and to improve our understanding of the global carbon cycle in a changing climate. I will discuss two inverse analyses that use these observations to estimate greenhouse gas fluxes. First, I will present work that quantifies 2019 annual mean methane emissions in the contiguous US (CONUS) at 0.25° × 0.3125° resolution by inverse analysis of atmospheric methane columns measured by the Tropospheric Monitoring Instrument (TROPOMI). In this work, we optimize emissions and quantify observing system information content for an eight-member inversion ensemble through analytical minimization of a Bayesian cost function. We achieve high resolution with a reduced-rank characterization of the observing system that optimally preserves information content. Our optimal (posterior) estimate of anthropogenic emissions in CONUS is 13 % larger than the 2023 GHGI estimate for CONUS in 2019, with a 51% increase relative to the GHGI landfill estimate. To understand this discrepancy, we exploit the high resolution of our inversion to quantify emissions from 70 individual landfills, 48 individual states, and 95 geographically diverse urban areas in CONUS. Second, I will briefly discuss ongoing work to estimate monthly CO2 fluxes for 2015 to 2023 at 4° × 5° resolution globally constrained by atmospheric CO2 column observations from the Orbiting Carbon Observatory-2 (OCO-2) instrument.