Weakly Interacting Massive Particles (WIMPs) are among the main candidates for the relic dark matter (DM). The idea of the direct DM detection relies on elastic spin-dependent (SD) and spin-independent (SI) interaction of WIMPs with target nuclei. In this review paper the relevant formulae for WIMP event rate calculations are collected. For estimations of the WIMP-proton and WIMP-neutron SD and SI cross sections the effective low-energy minimal supersymmetric standard model is used. The traditional one-coupling-dominance approach for evaluation of the exclusion curves is described. Further, the mixed spin-scalar coupling approach is discussed. It is demonstrated, taking the high-spin Ge-73 dark matter experiment HDMS as an example, how one can drastically improve the sensitivity of the exclusion curves within the mixed spin-scalar coupling approach, as well as due to a new procedure of background subtraction from the measured spectrum. A general discussion on the information obtained from exclusion curves is given. The necessity of clear WIMP direct detection signatures for a solution of the dark matter problem, is pointed out.
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