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Byline: P. Ciais (1), P. Rayner (1), F. Chevallier (1), P. Bousquet (1), M. Logan (1), P. Peylin (1,2), M. Ramonet (1) Abstract: We provide a review description of atmospheric inversion methods for the determination of fluxes of long-lived trace gases based on measurements of atmospheric concentration. Emphasis is given to technical aspects of inversion settings, which are crucial to inter-compare and understand inversion results. We briefly sketch the formalism used in such methods, then provide a summary of major currents in research and contemporary problems. Most attention is given to carbon dioxide (CO.sub.2) which poses the threat of future climate change. Therefore, there is keen interest in better understanding where and when CO.sub.2 emitted by the combustion of fossil fuels is reabsorbed by land ecosystems and oceans. Using the information contained in concentration fields observed from ground-based networks and from upcoming satellite observations in order to constrain the geographic distribution of surface fluxes is an inverse problem it consists of finding a set of fluxes that optimally matches the observations available. We review the application of inverse methods to quantify the distribution of the sources and sinks of CO.sub.2 at the surface of the Earth based on global measurements of atmospheric concentration and three-dimensional models of atmospheric transport. We describe the use of top--down atmospheric inversion methods in terms of numerical transport modeling and atmospheric observation networks, and detail some of the currently important issues in assigning uncertainties. Author Affiliation: (1) Unite Mixte de Recherche LSCE, CEA-CNRS-UVSQ, Batiment 709, CE Orme des Merisiers, 91191, Gif sur Yvette, France (2) Unite Mixte de Recherche BioMCo, INRA-CNRS-INAPG, Universite Paris 6, Batiment EGER, 78850, Thivernal-Grignon, France Article History: Registration Date: 22/06/2010 Received Date: 05/01/2009 Accepted Date: 15/06/2010 Online Date: 20/07/2010