[en] The recent discovery of the Higgs boson completes the standard model of particle physics, but no compelling signal for physics beyond the standard model has been observed despite the numerous searches performed by experiments at the Large Hadron Collider (LHC). Nevertheless, the hierarchy problem and the observation of dark matter are compelling arguments to study theories predicting new states at the weak scale, and a main effort has been directed towards understanding the negative search results and their implications for such weak scale new physics scenarios. Simplified models have become a standard in the interpretation of LHC searches for supersymmetry (SUSY), aiming at maximal model independence. More recently a similar approach was adopted for the interpretation of dark matter searches. The success of this approach is due to the fact that the small set of free parameters relates to the observables in LHC searches in a clear way, allowing an efficient optimisation of search strategies. Moreover, generic models can be projected on a simplified model description giving an intuitive understanding of the constraints on the parameter space, and providing a fast test against LHC constraints. As the relation between generic model parameters and simplified models is generally not straightforward, sophisticated computational tools are required to facilitate such a projection. This thesis explores the various aspects of simplified model interpretations of LHC searches and how they can be used to understand the results and bridge the gap between theoretical descriptions and experimental observations. In particular the software tool SMODELS is presented, a tool that automates the mapping of generic models onto SUSY-like simplified model components, and that allows direct tests against corresponding experimental limits in the included database. Under certain assumptions SMODELS can be used to constrain a wide class of new physics models with a dark matter candidate. These assumptions and some explicit tests are discussed in detail, followed by studies of (non-minimal) supersymmetric models using SMODELS for the fast evaluation of constraints from SUSY searches. These studies highlight the capacity as well as the limitations of using simplified model results to study generic models. Finally regarding simplified models for dark matter searches, scenarios with a spin-2 mediator are studied in detail. (author)