A brief review is given of the effects of CP violation on the direct
detection of neutralinos in dark matter detectors. We first summarize the
current developments using the cancellation mechanism which allows for the
existence of large CP violating phases consistent with experimental limits on
the electron and on the neutron electric dipole moments in a broad class of
SUSY, string and D brane models. We then discuss their effects on the
scattering of neutralinos from quarks and on the event rates. It is found that
while CP effects on the event rates can be enormous such effects are reduced
significantly with the imposition of the EDM constraints. However, even with
the inclusion of the EDM constraints the effects are still very significant and
should be included in a precision prediction of event rates in any SUSY, string
or D brane model.Comment: Based on an invited talk at the conference "Sources and Detection of
Dark Matter in the Universe", at Marina del Rey, CA, Feb. 23-25, 2000; 12
pages, Latex including 2 figure
