  The detection of the theoretically expected dark matter is central to
particle physics cosmology. Current fashionable supersymmetric models provide a
natural dark matter candidate which is the lightest supersymmetric particle
(LSP). Such models combined with fairly well understood physics like the quark
substructure of the nucleon and the nuclear form factor and the spin response
function of the nucleus, permit the evaluation of the event rate for
LSP-nucleus elastic scattering. The thus obtained event rates are, however,
very low or even undetectable. So it is imperative to exploit the modulation
effect, i.e. the dependence of the event rate on the earth's annual motion. In
this review we study such a modulation effect in directional and undirectional
experiments. We calculate both the differential and the total rates using
symmetric as well as asymmetric velocity distributions. We find that in the
symmetric case the modulation amplitude is small, less than 0.07. There exist,
however, regions of the phase space and experimental conditions such that the
effect can become larger. The inclusion of asymmetry, with a realistic enhanced
velocity dispersion in the galactocentric direction, yields the bonus of an
enhanced modulation effect, with an amplitude which for certain parameters can
become as large as 0.46.
