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The chemical compositions of stars encode the history of the universe and are thus fundamental for advancing our knowledge of astrophysics and cosmology. However, measurements of elemental abundance ratios, and our interpretations of them, strongly depend on the physical assumptions that dictate the generation of synthetic stellar spectra. Three-dimensional radiation-hydrodynamic (3D RHD) box-in-a-star simulations of stellar atmospheres offer a more realistic representation of surface convection occurring in late-type stars than do traditional one-dimensional (1D) hydrostatic models. As evident from a multitude of observational tests, the coupling of 3D RHD models with line formation in nonlocal thermodynamic equilibrium (non-LTE) today provides a solid foundation for abundance analysis for many elements. This review describes the ongoing and transformational work to advance the state of the art and replace 1D LTE spectrum synthesis with its 3D non-LTE counterpart. In summary:
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