This thesis deals with Dark Matter (DM) properties, mainly in the context of the Next-to-Minimal Supersymmetric Standard Model (NMSSM). First, it is examined whether a neutralino in the NMSSM could explain a monochromatic photon excess possibly present in the Fermi-LAT data. It is shown that neutralino pair annihilation with a CP-odd Higgs exchanged in s-channel can, in principle, give rise to a sufficiently large cross section. Asymmetric dark matter models, aiming at the explanation of the coincidence of present-day DM and baryon abundances, are also discussed. Upper bounds on DM self-annihilation cross section, which can potentially destroy the DM asymmetry, are derived and applied to a variety of models. Finally, a supersymmetric model is proposed, providing sneutrinos as viable asymmetric DM and explaining the smallness of neutrino masses. Bounds on this model from particle physics, cosmology and DM searches are studied.
