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Supersymmetric Dark Matter candidates in light of constraints from collider and astroparticle observables

The Standard Model of particle physics has been strengthened by the recent discovery of the long-awaited Higgs boson. The standard cosmological model has met the challenge of the high precision observations in cosmology and astroparticle physics. However these two standard models face both several theoretical issues, such as the naturalness problem in the Higgs sector of the Standard Model, as well as observational issues, in particular the fact that an unknown kind of matter called Dark Matter accounts for the majority of the matter content in our Universe. Attempts to solve such problems have led to the development of New Physics models during the last decades. Supersymmetry is one such model which addresses the fine-tuning problem in the Higgs sector and provides viable Dark Matter candidates. Current high energy and high precision experiments give many new opportunities to probe the supersymmetric models. It is in this context that this thesis is written. Considering the Minimal Supersymmetric Standard Model (MSSM), the simplest supersymmetric extension of the Standard Model of particle physics, and its conventional Dark Matter candidate, the neutralino, it is shown that collider constraints could provide informations on the very early Universe at the inflation area. It is also demonstrated that the Indirect Detection of Dark Matter, despite several drawbacks, can be a powerful technique to probe supersymmetric Dark Matter models. Beyond the MSSM it is shown that unique characteristics of the Dark Matter candidate in the NMSSM could be probed at colliders. The study of a supersymmetric model with an extended gauge symmetry, the UMSSM, is also developed. The features of another Dark Matter candidate of this model, the Right-Handed sneutrino, are analysed. More general constraints such as those coming from low energy observables are finally considered in this model.