The Infrared Atmospheric Sounding Interferometer (IASI) is a Fourier Transform Spectrometer implemented on the MetOp satellite series. The instrument is intended to measure infrared radiation emitted from the Earth. IASI produces data with unprecedented accuracy and spectral resolution. Notably, the sounder harvests spectral information to derive temperature and moisture profiles, as well as concentrations of trace gases, essential for the understanding of weather, for climate monitoring, and for atmospheric forecasts. The large spectral, spatial, and temporal resolution of the data collected by the instrument involves generating products with a considerably large size, about 16 Gigabytes per day by each of the IASI-A and IASI-B instruments currently operated. The amount of data produced by IASI demands efficient compression techniques to improve both the transmission and the storage capabilities. This thesis supplies a comprehensive analysis of IASI data compression and provides effective recommendations to produce useful reconstructed spectra. The study analyzes data at different processing stages. Specifically, we use data transmitted by the instrument to the reception stations (IASI L0 products) and end-user data disseminated to the Numerical Weather Prediction (NWP) centres and the scientific community (IASI L1C products). In order to better understand the nature of the data collected by the instrument, we analyze the information statistics and the compression performance of several coding strategies and techniques on IASI L0 data. The order-0 entropy and the order-1, order-2, and order-3 context-based entropies are analyzed in several IASI L0 products. This study reveals that the size of the data could be considerably reduced by exploiting the order-0 entropy. More significant gains could be achieved if contextual models were used. We also investigate the performance of several state-of-the-art lossless compression techniques. Experimental results suggest that a compression ratio of 2. 6:1 can be achieved, which involves that more data could be transmitted at the original transmission rate or, alternatively, the transmission rate of the instrument could be further decreased. A comprehensive study of IASI L1C data compression is performed as well. Several state-of-the-art spectral transforms and compression techniques are evaluated on IASI L1C spectra. Extensive experiments, which embrace lossless, near-lossless, and lossy compression, are carried out over a wide range of IASI-A and IASI-B orbits. For lossless compression, compression ratios over 2. 5:1 can be achieved. For near-lossless and lossy compression, higher compression ratios can be achieved, while producing useful reconstructed spectra. Even though near-lossless and lossy compression produce higher compression ratios compared to lossless compression, the usefulness of the reconstructed spectra may be compromised because some information is removed during the compression stage. Therefore, we investigate the impact of near-lossless and lossy compression on end-user applications. Specifically, the impact of compression on IASI L1C data is evaluated when statistical retrieval algorithms are later used to retrieve physical information. Experimental results reveal that the reconstructed spectra can enable competitive retrieval performance, improving the results achieved for the uncompressed data, even at high compression ratios. We extend the previous study to a real scenario, where spectra from different disjoint orbits are used in the retrieval stage. Experimental results suggest that the benefits produced by compression are still significant. We also investigate the origin of these benefits. On the one hand, results illustrate that compression performs signal filtering and denoising, which benefits the retrieval methods. On the other hand, compression is an indirect way to produce spectral and spatial regularization, which helps pixel-wise statistical algorithms.