This contribution lays out the scientific foundations of the project ExoMol. This projectwill produce molecular line lists for all molecules considered to be important for themodelling atmospheres of exoplanets and cool stars, which are prerequisites for thespectroscopic characterization of the atmospheres of these astrophysical objects. Towardsthis end 25 species are identified as key ones for meeting current demands for atmosphericmodels of exoplanets and brown dwarfs, impeded by the lack of fundamental data on theabsorption of these species. The production of comprehensive and very largerotation-vibration and rotation-vibration-electronic line lists requires a mixture offirst principles quantum mechanical methods and empirical tuning based on laboratoryspectroscopic data. ExoMol will rely on these methodologies and make extensive use ofstate-of-the-art computing.