  We review various issues related to the direct detection of constituents of
dark matter, which are assumed to be Weakly Interacting Massive Particles
(WIMPs). We specifically consider heavy WIMPs such as: 1) The lightest
supersymmetric particle LSP or neutralino. 2) The lightest Kaluza-Klein
particles in theories of extra dimensions and 3) other extensions of the
standard model. In order to get the event rates one needs information about the
structure of the nucleon as well as as the structure of the nucleus and the
WIMP velocity distribution. These are also examined
  Since the expected event rates for detecting the recoiling nucleus are
extremely low and the signal does not have a characteristic signature to
discriminate them against background we consider some additional aspects of the
WIMP nucleus interaction, such as the periodic behavior of the rates due to the
motion of Earth (modulation effect). Since, unfortunately, this is
characterized by a small amplitude we consider other options such as
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.
