  This paper, based on a presentation at the Spintronics 2001 conference,
provides a review of our studies on II-VI and III-V Mn-doped Diluted Magnetic
Semiconductors. We use simple models appropriate for the low carrier density
(insulating) regime, although we believe that some of the unusual features of
the magnetization curves should qualitatively be present at larger dopings
(metallic regime) as well. Positional disorder of the magnetic impurities
inside the host semiconductor is shown to have observable consequences for the
shape of the magnetization curve. Below the critical temperature the
magnetization is spatially inhomogeneous, leading to very unusual temperature
dependence of the average magnetization as well as specific heat. Disorder is
also found to enhance the ferromagnetic transition temperature. Unusual spin
and charge transport is implied.
