Résumé : Despite the compelling amount of evidence for the presence of dark matter in our universe through gravitational effects, the exact nature of dark matter is still one of the main open questions in modern physics. A great experimental effort has been performed in order to probe one of the most well studied dark matter candidates, the Weakly Interacting Massive Particle or WIMP. Despite many searches performed, there has not been any conclusive detection of dark matter yet. Hence, these searches place strong constraints on the WIMP paradigm, restricting the amount of models containing a viable WIMP candidate. The community has therefore started to consider different dark matter candidates who are able to evade the strong experimental constraints.A novel dark matter candidate that has gained a lot of attention in the recent years is the Feebly Interacting Massive Particle or FIMP. Unlike the WIMP, which is produced through the freeze-out mechanism, for which it needs sizable interactions with the standard model particles, the FIMP has very feeble interactions. The FIMP is therefore unable to reach a state of equilibrium which is needed in order to be produced trough freeze-out. There is a variety of mechanisms able to produce the correct amount of FIMPs to explain all the dark matter in our universe, despite its feeble interactions. 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.