Solar photosphere and chromosphere are composed of weakly ionized plasma for which collisional coupling decreases with height. This implies a breakdown of some hypotheses underlying magnetohydrodynamics at low altitudes and gives rise to non-ideal MHD effects such as ambipolar diffusion, Hall effect, etc. Recently, there has been progress in understanding the role of these effects for the dynamics and energetics of the solar atmosphere. There are evidences that phenomena such as wave propagation and damping, magnetic reconnection, formation of stable magnetic field concentrations, magnetic flux emergence, etc can be affected. This paper reviews the current state-of-the-art of multi-fluid MHD modeling of the coupled solar atmosphere.