The temperature and density conditions in the magnetized photosphere and chromosphere of the Sun lead to a very small degree of atomic ionization. At particular heights, the magnetic field may be strong enough to give rise to a cyclotron frequency larger than the collisional frequency for some species. These circumstances influence the collective behavior of the particles and some of the hypotheses of magnetohydrodynamics may be relaxed, giving rise to non-ideal MHD effects. In this paper we discuss our recent developments in modeling non-ideal plasma effects, as well as their observational consequences.