Molecules in stellar atmospheres play key roles, not only as promoters of our understanding of stars, but also as actors affecting the structures of the atmospheres. In particular cool star atmospheres are affected by molecular opacities, and during recent years it has become clear that also weak molecular lines are of crucial structural importance. Extensive molecular data are thus needed in order to correctly model the structure of a stellar atmosphere and the transport of radiation through it. The basis for how such molecular data are acquired constitutes the theme of the present article. As will follow below, results from different subfields of molecular physics are needed in order to obtain a complete picture of the absorption of radiation by molecules. This article will only consider allowed molecular electronic transitions, i.e. dipole transitions between different electronic states; however, the presentation and the formulae may easily be modified to be valid for transitions between levels within a single electronic state.