  Various issues related to the direct detection of supersymmetric dark matter
are reviewed. Such are: 1) Construction of supersymmetric models with a number
of parameters, which are constrained from the data at low energies as well as
cosmological observations. 2) A model for the nucleon, in particular the
dependence on the nucleon cross section on quarks other than u and d. 3) A
nuclear model, i.e. the nuclear form factor for the scalar interaction and the
spin response function for the axial current. 4) Information about the density
and the velocity distribution of the neutralino (halo model). Using the present
experimental limits on the rates and proper inputs in 3)-4) we derive
constraints in the nucleon cross section, which involves 1)-2). Since the
expected event rates are extremely low we consider some additional signatures
of the neutralino nucleus interaction, such as the periodic behavior of the
rates due to the motion of Earth (modulation effect), which, unfortunately, is
characterized by a small amplitude. This leads us to examine the possibility of
suggesting directional experiments, which measure not only the energy of the
recoiling nuclei but their direction as well. In these, albeit hard,
experiments one can exploit two very characteristic signatures: a)large
asymmetries and b) interesting modulation patterns. Furthermore we extended our
study to include evaluation of the rates for other than recoil searches such
as: i) Transitions to excited states, ii) Detection of recoiling electrons
produced during the neutralino-nucleus interaction and iii) Observation of hard
X-rays following the de-excitation of the ionized atom.
