Beyond the Standard Model: phenomenology and LHC constraints of exotic dark matter

The Standard Model (SM) of particle physics is one of the most successful theories in science. Indeed, numerous SM predictions have been observed to be consistent with experimental measurements. However, some caveats hint at the incompleteness of the SM and push physicists to search for new physics. The ATLAS and CMS collaborations are carrying out an extensive and exciting physics program at the LHC. Searches for new physics constitute a relevant part of this program. Simplified models are used to characterize the potential new physics signal. Reinterpreting the LHC results in more realistic scenarios than the simplified models is crucial to use most of the physics sensitivity of the data. The work of this thesis focused on two aspects of reinterpretation, the improvement of reinterpretation tools and the phenomenology of models beyond the Standard Model (BSM). The statistical combination of signal regions (SRs) allows using more of the physics sensitivity of the experimental data in public tools. This thesis participated in the implementation of this feature in MadAnalysis5 and SModelS. Part of the focus was also given to phenomenological studies to demonstrate the impact of SR combination. Explaining the nature of dark matter (DM) is another area where the SM fails. Although many hypothetical particles with different properties are good DM candidates, the way they are produced in the early Universe can be classified into a few main mechanisms. The standard WIMP picture is based on the freeze-out mechanism, which is based on several assumptions that are valid in general cases. However, these assumptions can be broken for some scenarios, leading to exceptions to the standard WIMP picture. The DM portion of this thesis focused on a recently proposed mechanism, which is the conversion-driven freeze-out mechanism. (author)