The purpose of the present paper is to provide an overview of As
ymptotic-
Preserving methods for multiscale plasma simulations by ad
dressing three sin-
gular perturbation problems. First, the quasi-neutral lim
it of fluid and kinetic
models is investigated in the framework of non magnetized as
well as magne-
tized plasmas. Second, the drift limit for fluid description
s of thermal plasmas
under large magnetic fields is addressed. Finally efficient nu
merical resolutions
of anisotropic elliptic or diffusion equations arising in ma
gnetized plasma simu-
lation are reviewed.