"The compilation of the recent cosmological data from experiments in cosmology and astrophysics, and in particular of those of the WMAP satellite, confirm with greater accuracy the standard cosmological model. According to them the current energy density of the Universe is comprised by about 70% of dark energy and 30% of matter, most of which is in the form of non-baryonic dark matter (DM). It has been appreciated for some time that the lightest supersymmetric particle (LSP) is a suitable candidate for this non-baryonic cold dark matter. The LSP is stable in supersymmetric models where R-parity is conserved, and its relic density falls naturally within the favoured range if it weighs less than 1 TeV. In this case the most of the parameter space of the supersymmetric models can be explored by the future high energy experiments, like these that will be performed at LHC collider at CERN after about two years and at the International Linear Collider some years later. This, in conjunction with the upcoming information from projects like the PLANCK satellite and the various neutrinos telescopes, will provide us with the unique opportunity to comprehend the fundamental physics beyond the Standard Model of the particle physics. We will study the effect of the presence of CP violating phases on direct and indirect DM experiments, in the context of variants of the Minimal Supersymmetric Standard Model (MSSM), and we will impose the cosmological constraints by estimating precisely the neutralino relic density. In doing so, we will explore the complementarity between the accelerator and DM searches. In addition, we will investigate the possibility of baryogenesis through leptogenesis in this framework. On the other hand, we will study the possibility that the LSP is the gravitino, the supersymmetric partner of the graviton, and we will explore the interplay between the DM and the Dark Energy, in the context of grand unified and string models."