  In this thesis we use the Effective Field Theory approach for supersymmetric
theories, applied to two experimental domains : the search for the Higgs bosons
at colliders and the Dark Matter observables. The reason for introducing an
effective approach in the Higgs physics is that the simple supersymmetric
extension of the Standard Model (the MSSM) is known to have a tightly
constrained Higgs sector, in particular with a lightest Higgs mass difficult to
raise without introducing some fine-tuning. Many specific expansions (as the
NMSSM for instance) allow for a richer Higgs sector. In this case however, the
effective approach is handy since it encompasses many different specific
ultraviolet completions. We have added to the Kahler and superpotential of the
MSSM all possible terms of dimensions 5 and 6 including only Higgs superfields.
The phenomenology of the resulting Higgs sector appears to be much richer, and
we analyse our model in view of the latest LHC results. On the other side,
supersymmetry is known for providing a Dark Matter candidate, so we have also
worked to improve the accuracy of the computation of the relic density in the
MSSM. Indeed the impressive accuracy on the experimental side (around 6%) calls
for a precise computation including radiative corrections. Those one-loop
computations being rather long in the MSSM, thus often overlooked, we have used
again the effective approach by introducing new effective vertices that aim at
accounting for the one-loop correction. We show on a specific process
(neutralinos annihilation to muons) the agreement between the effective
approach and the full one-loop computation.
