Physics beyond the Standard Model can appear as new particles too heavy to be produced in experiments (the energy frontier) or interacting too weakly to be seen in our measurements (the intensity frontier). In the first part of this thesis, we study two dark matter models of electroweak WIMP coming from two limiting cases in the MSSM: the Higgsino and the Wino model. The dark matter candidate is a particle too heavy to be directly seen in colliders but it could be seen indirectly by astrophysical observations. Dark matter particles in the galaxy can annihilate to Standard Model particles and be detected by satellites. We consider the charged neutral mass splitting as a free parameter in the theory and investigate its effect on the Sommerfeld enhancement which gives an important boost to the annihilation cross-section, the main observable of indirect detection. In the second part of this thesis, we present an idea of a fixed target experiment so search for dark sector models, a class of model with very weakly interacting particles. This experiment uses the experimental setup needed for a future muon collider but is independent from the muon collider program. We study the reach of our experiment for three benchmark models, the dark photon, the dark Higgs, the heavy neutral lepton and we compare its expected performances to current and future experiments. In the third part of this thesis, we consider a more model-independent approach to the search for new physics. If new states are heavy, they can be integrated out and their leading effects are encoded in effective operators made of Standard Model fields. Assuming baryon and lepton number conservation, one can classify the effective operators of dimension-6 which give the leading contribution and constrain the coefficient of these operators by looking at precision observables. We compile results from LEP-I and LEP-II experiments as well as neutrino scattering and other low-energy observables. We allow all operators to be present with an arbitrary flavour structure. Our result can then be used to translate these constaints to specific models of new physics.