The LHC has provided a staggering number of searches for physics beyond the Standard Model. However the valuable information contained in these results is unavoidably fragmented into multiple analyses, each constraining different specific models. In this talk I will illustrate how it has become increasingly more necessary for theorists to perform extrapolations of (``reinterpret'') the experimental analyses, in order to fully grasp the consequences of the LHC searches for theoretical panorama of new physics models. Drawing from my past experience, I will describe some of the challenges faced in this kind of studies and the lessons learned out of the LHC Run I results, from the status of weak-scale supersymmetry to searches for Dark Matter at colliders. I will also present some of the tools I have been developing to simplify these reinterpretation activities.