Most of the visible light coming from the Sun originates in the solar photosphere. Numerical simulations are a common tool to study the solar atmosphere starting from the basic laws of physics and few additional assumptions. This thesis presents results of three-dimensional radiative magnetohydrodynamic simulations of the quiet-sun, plage and sunspot umbra. These simulations are used to compute synthetic observations that can be compared to the real observations. Each chapter of this thesis tackles a different problem: the solar abundance of indium, the formation of the only photospheric spectral line that shows activity variation, the formation of the spectral lines in the horizontal supersonic flows caused by convective motions, the center-to-limb variation of the emergent continuum and the spectropolarimetric diagnostic of the simulated sunspot umbra.