The solar chromosphere represents a formidable modelling challenge. It is highly dynamic and structurally complex, due to constant motions of the magnetic field, with spicules, shocks, swirls and jets providing mass and energy high into the atmosphere. At the same time it departs from local thermodynamic equilibrium (LTE), the radiative cooling and heating is dominated by a few strong lines and time dependent ionisation becomes important. The radiative-MHD MURaM code now extends from the convection zone into the corona, including approximations to the important non-LTE processes similar to those used in Bifrost. Using 3D radiative transfer, the models now come close to reproducing the line width and intensities of the Mg II h&k lines. Other chromospheric lines and the millimetre continuum can also be reproduced. Dynamic events such as Spicules, long a puzzle for realistic models, now form naturally in the simulations.
Key discrepancies remain, however, and they point to a broader issue. The chromosphere and corona cannot be understood in isolation. All the energy that heats the corona passes through the chromosphere, while coronal heating and mass exchange in turn shape the chromosphere below. Resolving these discrepancies requires interpreting the photosphere, chromosphere and corona together. The photosphere, often underappreciated, supplies both the magnetic field and the motions that energise the layers above. Its local field strength and flux imbalance shape the chromosphere. This motivates systematic multi-height comparisons. At the same time, the non-LTE approximations used must be reassessed across the range of conditions the models now reach. Addressing this problem requires a new generation of GPU accelerated non-LTE radiative-MHD codes.