The MESSIER satellite has been designed to explore the extremely low surface brightness universe at UV and optical wavelengths. The two driving science cases target the mildly- and highly non-linear regimes of structure formation to test two key predictions of the LCDM scenario: (1) the detection of the putative large number of galaxy satellites, and (2) the identification of the filaments of the cosmic web. The satellite will drift scan the entire sky in 8 bands covering the 200-900 nm range to reach the unprecedented surface brightness levels of 32 mag/arcsec^2 in the optical and 37 mag/arcsec^2 in the UV. Many important secondary science cases will result as free by-products and will be discussed in some detail, such as the luminosity function of galaxies, the contribution and role of intracluster light, the cosmological background radiation at UV and optical wavelengths, the molecular hydrogen content of galaxies at z=0.25, the chemical enrichment of the interstellar medium through mass loss of red giant stars. It will also provide the first space-based reference UV-optical photometric catalogue of the entire sky, and synergies with GAIA and EUCLID will also be discussed.