There are a number of various observation, which indicate the presence of Dark Matter (DM), one of the biggest mysteries of modern Cosmology. Recent cosmological observations suggest that the Matter-Energy density of the Universe is close to its critical density, Omega = 1, whose large, amount (similar or equal to70%) is Dark Energy of uknown origin. The baryonic density comprises only the similar or equal to 5% while the rest is due to Dark Matter of unknown composition. Modern particle physics theories, notably String Theories, should address to the question who ordered both Dark Energy and Dark Matter. In the framework of Supersymmetric theories the yet undiscovered in accelerator experiments "neutralinos" can be good candidates for Cold Dark Matter. Their relic density today can be in agreement with astrophysical data constraining, if combined with other data from accelerator experiments, the predictions of supersymmetric models. This is of relevance for future planned experiments which will search for Supersymmetry.