[en] This paper lays down the theoretical bases and the methods used in the Fast Optimal Retrievals on Layers for IASI (FORLI) software, which is developed and maintained at the “Université Libre de Bruxelles” (ULB) with the support of the “Laboratoire Atmosphères, Milieux, Observations Spatiales” (LATMOS) to process radiance spectra from the Infrared Atmospheric Sounding Interferometer (IASI) in the perspective of local to global chemistry applications. The forward radiative transfer model (RTM) and the retrieval approaches are formulated and numerical approximations are described. The aim of FORLI is near-real-time provision of global scale concentrations of trace gases from IASI, either integrated over the altitude range of the atmosphere (total columns) or vertically resolved. To this end, FORLI uses precalculated table of absorbances. At the time of writing three gas-specific versions of this algorithm have been set up: FORLI-CO, FORLI-O₃ and FORLI-HNO₃. The performances of each are reviewed and illustrations of results and early validations are provided, making the link to recent scientific publications. In this paper we stress the challenges raised by near-real-time processing of IASI, shortly describe the processing chain set up at ULB and draw perspectives for future developments and applications.