Numerical simulations of the solar chromosphere yield phyiscal quantities such as temperature, velocity and mass density. These cannot be directly compared to observations. In order to make such comparison one needs to compute synthetic observations from the simulations. For chromospheric spectral lines as Halpha, Ca II H&K, MgII h&k and, to a lesser extent, Ca II 854.2 nm these synthetic observations need to take both non-LTE and 3D effects into account.
I will give a brief overview of the numerical methods that are used to compute synthetic observations, with a focus on how to solve the radiative transfer equation in an efficient manner on supercomputers using domain decomposition. In addition, I will present results from such 3D non-LTE computations that explain the formation of the Halpha line, which is used as one of the main diagnostics of the solar chromosphere. If time permits I will also discuss the diagnostic potential of the MgII h&k lines, which will be observed with the upcoming IRIS satellite.