DescriptionIn this thesis, we study models of physics beyond the Standard Model (SM) at the electroweak scale and their phenomenology, motivated by naturalness and the nature of dark matter. Moreover, we introduce analyses and techniques relevant in searches at the Large Hadron Collider (LHC). We start by applying computer vision with deep learning to build a boosted top jets tagger at the LHC that outperforms previous state-of-the-art classifiers by a factor of ~2-3 or more in background rejection, over a wide range of tagging efficiencies. Next, we define a cut and count based analysis for supersymmetric top quarks at LHC Run II capable of probing the line in the mass plane where there is just enough phase space to produce an on-shell top quark from the stop decay. We also implement a comprehensive reinterpretation of the 13 TeV ATLAS and CMS searches with the first ~15/fb of data and derive constraints on various simplified models of natural supersymmetry. We discuss how these constraints affect the fine-tuning of the electroweak scale. Finally, we show how a simple extension of the minimal supersymmetric SM, consisting of a dark sector, can explain the dark matter relic abundance and the Higgs mass in a natural way.