  The purpose of the present paper is to provide an overview of
Asymptotic-Preserving methods for multiscale plasma simulations by addressing
three singular perturbation problems. First, the quasi-neutral limit of fluid
and kinetic models is investigated in the framework of non magnetized as well
as magnetized plasmas. Second, the drift limit for fluid descriptions of
thermal plasmas under large magnetic fields is addressed. Finally efficient
numerical resolutions of anisotropic elliptic or diffusion equations arising in
magnetized plasma simulation are reviewed.
