  Despite the compelling amount of evidence for the existence of dark matter,
its exact nature is still one of the main open questions in modern physics. A
great experimental effort has been performed to probe one of the most popular
dark matter candidates, the Weakly Interacting Massive Particle or WIMP,
however, there has not been any conclusive detection yet. Hence, these searches
place strong constraints on the WIMP paradigm. The community has therefore
started to consider alternatives who are able to evade the strong experimental
constraints. Such a candidate that has gained a lot of attention in the recent
years is the Feebly Interacting Massive Particle or FIMP. Unlike the WIMP, the
FIMP has very feeble interactions. It is therefore unable to reach a state of
equilibrium which is needed to be produced trough freeze-out. Despite these
feeble interactions, there is still a variety of mechanisms able to produce the
observed amount of dark matter in our universe. In this work, a selection of
these mechanisms, such as freeze-in or conversion driven freeze-out, are
discussed in detail. Since these FIMPs are so feebly interacting with standard
model particles, it is difficult to probe these particles through conventional
direct and indirect detection searches. In contrast, the feeble couplings give
rise to long-lived particles coupling to the DM, which can hence be smoking gun
signatures for FIMPs. This thesis will therefore focus on searches for
long-lived particles, both at hadron colliders and beam-dump experiments. In
order to do so, a classification of FIMP models has been put forward within the
context of this PhD, in which potential production mechanisms are identified in
order to define a viable parameter space. Within this framework, both existing
and potential future searches for long-lived particles are discussed and
applied to a subset of the proposed classification.
