The standard model of particle physics (SM) is arguably the best tested theory of physics, providing an accurate description of virtually all high energy particle physics phenomena observable in the laboratory. However, the SM also has a number of shortcomings: some of more theoretical nature such as the fine-tuning problem of the Higgs or the strong-CP problem, and some of more phenomenological nature such as not allowing for a satisfying implementation of neutrino masses and the lack of a suitable candidate for the observed dark matter of the Universe.

The SM’s shortcomings have motivated the development of a large number of beyond the SM (BSM) particle physics models. However, no (conclusive) evidence for any BSM model has been found to date. The papers included in this thesis study different approaches to search for BSM physics:

In [I], we studied bounds on weakly interacting massive particle (WIMP) DM models arising from the absence of neutrino signals from DM capture and subsequent DM pair-annihilation in dense astrophysical objects such as the Sun or the Earth. We interpreted these bounds in a model independent fashion, focusing in particular on the scaling of the bounds for the case where WIMPs comprise only a sub-dominant component of the DM. We also used a chemical composition of the Earth updated with respect to the previous literature, strengthening the bound on spin-dependent interactions from capture and annihilation in the Earth by approximately a factor 3.

In [II], we studied the collider phenomenology of one particular BSM model, the next-to-minimal supersymmetric standard model (NMSSM). In particular, we focused on 1) the impact of the presence of the 125 GeV SM-like Higgs boson on the NMSSM parameter space, 2) the identification of NMSSM specific search channels at the LHC which allow to effectively probe the NMSSM parameter space allowed by more conventional searches, and 3) an in-depth study of one of these search channels, the mono-Higgs signature. As shown in [II], this channel allows to probe the low tan β , large m_A regime which is difficult to probe with conventional searches, and in contrast to many conventional Higgs searches, the reach of the mono-Higgs channel improves significantly with the increased luminosity expected to be collected at the LHC in current and future runs.

The past ~ 50 years have seen a remarkable success of particle physics. In the 1970s, the Standard Model was formulated and in 2012 its final ingredient, the Higgs boson, was discovered at the Large Hadron Collider (LHC). The Standard Model describes virtually all particle physics observable in the laboratory. However, despite this success, the Standard Model has a number of shortcomings. Some problems stem from its mathematical structure, most famously the hierarchy problem. Further, the Standard Model fails to describe the composition of our Universe, for example, it cannot explain the observed Dark Matter. Thus, the need for physics beyond the Standard Model is clear. A long series of experiments has been conducted to search for this new physics. Alas, these experiments came up empty handed.This thesis discusses two lines of work: 1) Arguably, the Higgs sector of the Standard Model is its least constrained part and simultaneously intimately related to many of the Standard Model's shortcomings. We discuss models extending the Higgs sector, both in a general and in a supersymmetric setting, and how they can be probed at the LHC. 2) A century after the first evidence for Dark Matter emerged, we still don't know what it is made up of. We discuss some models for Dark Matter, including axions and a particular model for Weakly Interacting Massive Particle (WIMP) Dark Matter. Then, we present some methods to search for WIMP Dark Matter, focusing on paleo-detectors, a proposed method where one would search for the traces of WIMP-nucleus interactions left in ancient minerals.