This contribution lays out the scientific foundations of the project ExoMol. This project will produce molecular line lists for all molecules considered to be important for the modelling atmospheres of exoplanets and cool stars, which are prerequisites for the spectroscopic characterization of the atmospheres of these astrophysical objects. Towards this end 25 species are identified as key ones for meeting current demands for atmospheric models of exoplanets and brown dwarfs, impeded by the lack of fundamental data on the absorption of these species. The production of comprehensive and very large rotation-vibration and rotation-vibration-electronic line lists requires a mixture of first principles quantum mechanical methods and empirical tuning based on laboratory spectroscopic data. ExoMol will rely on these methodologies and make extensive use of state-of-the-art computing.