  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.
