In the past 20 years, the Standard Model (SM) of elementary particles and their interactions has provided an unfailing description of all experimental observations at energy scales of ~100 GeV. The Large Hadron Collider of CERN was conceived to probe the physics of the TeV energy scale, providing a definitive statement on the infamous Higgs boson of the SM, but also looking for ``new physics''. And whereas the discovery of a Higgs boson in 2012 has completed the SM, there are several indications that such physics ``beyond the SM'' should exist. The possibilities are a testament to human ingenuity: from supersymmetry, which may blur the distinction between matter and force, to extra dimensions, which may provide the missing link between the standard model and gravity, there are numerous hypothesized new signals to search for. The LHC experiments are currently combing through their data samples looking for these new phenomena, and more. The talk will present a broad-brush picture of ``the why, the what and the how'' the searches are carried out, along with highlights of current results and the reasons for which expectations remain very high.