Dark Matter phenomenology : from simplified WIMP models to refined
  alternative solutions
  One of the most puzzling problems of modern physics is the identification of
the nature a non-relativistic matter component present in the universe,
contributing to more than 25$\%$ of the total energy budget, known as Dark
Matter. Weakly Interacting Massive Particles (WIMPs) are among the best
motivated dark matter candidates. However, in light of non conclusive detection
signals and strong constraints from collider, direct and indirect detection
experiments, this thesis presents constraints on several realizations of the
WIMP paradigm in the context of simplified dark matter models. More elaborated
models considering extended gauge structures are discussed further on, such as
constructions involving generalized Chern-Simons couplings and a specific WIMP
scenario motivated by recently observed flavour anomalies related to the
$R_{K^{(*)}}$ observable. The second part of this thesis is devoted to the
discussion of an alternative dark matter thermal production mechanism where an
explicit realization of the Strongly Interacting Massive Particles (SIMPs)
paradigm is discussed in the context of a non-Abelian hidden gauge structure.
In a last part, the possibility of producing non-thermally a dark matter
component via the "freeze-in" mechanism was investigated and the strong impact
of the post-inflationary reaheating stage of the universe on such constructions
illustrated by the specific case where dark matter density production is
mediated by a heavy spin-2 field in addition to the standard graviton.
