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We briefly review some theoretical issues involved in the direct detection ofsupersymmetric (SUSY) dark matter. After a brief discussion of the allowed SYSYparameter space we focus on the determination of the traditional neutralinodetection rates, in experiments which measure the energy of the recoilingnucleus, such as the coherent and spin induced rates and the dependence of therate on the motion of the Earth (modulation effect). Then we examine the novelfeatures appearing in directional experiments, which detect the recoilingnucleus in a given direction. Next we estimate the branching ratios fortransitions to accessible excited nuclear levels. Finally we estimate the eventrates leading to the atom ionization and subsequent detection of the outgoingelectrons.Comment: LaTex, 15 pages, 3 PostScript figure

SOME ISSUES RELATED TO THE DIRECT DETECTION OF SUSY DARK MATTER.