At elevated temperatures the spectra of polyatomic molecules become extremely complicated with millions, or even billions, of transitions potentially playing an important role. The atmospheres of cool stars and “hot Jupiter” extrasolar planets are rich with molecules in the temperature range 1000 to 3000 K and their properties are strongly influenced by the infrared and visible spectra of these molecules. Access to extensive lists of transitions is essential for interpreting even the rather simple spectra that can be obtained from exoplanets. So far there are extensive, reliable lists of spectral lines for a number species including some stable diatomics, water and ammonia. Data are almost completely lacking for many key species such as methane. The ExoMol project aims to construct line lists of molecular transitions suitable for spectroscopic and atmospheric modelling of cool stars and exoplanets. At high temperatures it is necessary to consider huge numbers of lines even for a single species. Examples of line lists are given; data protocols defined and data handling issues which arise from trying to distribute these huge datasets discussed. In particular, a uniform but flexible format is given for the representation of line lists and cross sections resulting from the ExoMol project.