Stellar spectral lines are now routinely measured at accuracies of 1% or better (<0.01 dex). However, systematic errors in modelling dominate the interpretation, and the errors in derived properties such as the abundance of a chemical element, are at least an order of magnitude larger, usually ~25% (0.1 dex). Advances in the accuracy of interpretation of stellar spectra will little doubt, as they have in the past and continue to do, provide insight into many current problems in astrophysics: the formation and evolution of stellar systems and planets, the origin and evolution of the chemical elements, characterisation of the first stars, and the formation and evolution of the Milky Way (via so-called “Galactic archeology”), to name some examples. The outlook for the future is especially bright when coupled to forthcoming accurate astrometric data from Gaia, and large-scale high-resolution spectroscopic surveys of the Galaxy such as that to be performed with the 4-metre Multi-Object Spectroscopic Telescope (4MOST).
Progress towards modelling spectra of cool stars (F,G,K) at the 1% accuracy level will be discussed. In particular I show results for modelling the Mg spectrum of cool stars in non-LTE with only atomic data from experiment or calculated quantum mechanically from first principles, i.e. without free parameters, such as scaling of collision rates from simple classical descriptions. I will also report on work to extend such work to all atoms, including some first results for complex atoms such as Fe. I will also discuss some other issues that currently limit the accuracy of stellar spectroscopy.