Realistic numerical simulations of the solar atmosphere can be used to interpret different phenomena observed on the solar surface. To gain insight into the atmospheric physical conditions, we compare the observations with 3D radiative magnetohydrodynamic models combined with forward modeling (radiative transfer). This thesis focuses particularly on the less understood chromospheric layer between the photosphere and the transition region. Only a few and complex spectral lines can probe the chromosphere making its observations a real challenge.The chromospheric environment is strongly influenced by departures from local thermodynamic equilibrium (non-LTE), horizontal radiative transfer (3D effects), and partially-coherent scattering of photons (partial redistribution effects). All these effects make the detailed 3D non-LTE radiative transfer very computationally demanding.In paper I, we focus on increasing the efficiency of non-LTE modeling of spectral lines in realistic solar models. We implemented a non-linear multigrid solver into the Multi3D code and showed that the method can handle realistic model atmospheres produced by radiative-MHD simulations. We obtained a speed-up of a factor 4.5-6 compared to multilevel accelerated lambda iteration.In paper II, we studied the chromospheric resonance lines Ca \textsc{ii} H\&K. Understanding their formation is crucial to interpreting the observations from the new imaging spectrometer CHROMIS, recently installed at the Swedish 1-m Solar Telescope. We investigated how the synthetic observables of Ca \textsc{ii} H\&K lines are related to atmospheric parameters.In paper III, we investigated a simulated active region including flux emergence that produced a flare. We modeled strong chromospheric lines, such as Ca \textsc{ii} H\&K, 8542 \AA, Mg \textsc{ii} h\&k, and H-$\alpha$, to investigate how it appears in synthetic images and spectra.