The visible atmosphere of the Sun (and other stars) is a sufficiently complex physical system that quantitative knowledge of its state can only be extracted from the observed spectrum of sunlight by computational modelling of the atmosphere and the spectrum. Such models have necessarily made use of simplifying approximations to make the modelling computationally feasible at the expense of the realism of the models. I report on progress in one particular area of realism: the computation of the equilibrium state of the gas and radiation field in a way that allows for non-local effects in the interaction of the gas particles and the radiation field (non-local thermodynamic equilibrium (NLTE)) in \approx 10^5 atomic line transitions. This involves solving a set of \approx 1200 coupled rate equations self-consistently, and is only feasible with parallelization and efficient numerical algorithms such as operator splitting. The inferred chemical composition of the Sun?s atmosphere is one major solar parameter that depends on inclusion of NLTE effects in the modelling.