Spectroscopy of late-type stars is usually based on one-dimensional (1D) hydrostatic model atmospheres and local thermodynamic equilibrium (LTE). It has recently become possible to relax both assumptions simultaneously, with the development of grids of 3D radiative-hydrodynamic model stellar atmospheres (Stagger/CIFIST), efficient codes for 3D multi-level non-LTE radiative transfer (Multi3D), and new, realistic models for inelastic low-energy collisions.

I shall discuss the state-of-the-art, in the context of ongoing work on three of the most important elements in astronomy: hydrogen, oxygen, and iron. 3D non-LTE effects on HI Balmer lines have a moderate impact on effective temperature determinations (~100 K), growing towards hotter and more metal-poor stars. First-principles modelling of the OI 777nm triplet, employing realistic inelastic O+e and O+H cross-sections, implies an uncomfortably low solar oxygen abundance (~8.55 dex), suggesting that some physics is missing from the spectroscopic models. Non-LTE overionisation of FeI is compounded by 3D effects, indicating that the metallicities of metal-poor stars are being systematically underestimated by both 1D LTE and 1D non-LTE studies.