The Standard Model (SM) of particle physics is remarkably successful and has survived two decades of precision tests at high energy particle accelerators. However, it is known to be incomplete, and there are reasons to believe that there is new physics at energy scales that will soon be probed in greater detail than ever before by the Large Hadron Collider (LHC), a proton-proton accelerator being built near Geneva.This thesis contains a diverse set of topics that may broadly be described as physics beyond the SM.In Chapter 2, implications of current experimental constraints are presented for the stop masses and mixing in the Minimal Supersymmetric Standard Model (MSSM), a well-motivated candidate for physics beyond the SM. It is found, for example, that lower bounds on the stop masses are as large as 1 TeV assuming no stop-mixing.Chapter 3 presents the regions in the MSSM with the minimal amount of fine-tuning of electroweak symmetry breaking. The minimal amount of tuning increases enormously for a Higgs mass beyond 120 GeV.Supersymmetry cannot be an exact symmetry, and one possibility is that our Universe is in a long-lived metastable state with broken supersymmetry. In Chapter 4, a generic model with this property is constructed in which all the relevant parameters, including the supersymmetry breaking scale, are generated dynamically. This model has several interesting model-building features including an explicitly and spontaneously broken R-symmetry, a singlet, a large global symmetry, naturalness, renormalizability, and a "pseudo-runaway'' direction.In Chapter 5, a simple extension of the SM with weakly interacting non-chiral dark matter particles is presented. Such particles can be detected at a future direct-detection experiment.There are a wide variety of possible discovery signatures for new physics at the LHC. A discovery signature with a large SM background that has not been well studied involves multi-jet events without leptons and/or missing energy.In Chapter 6, it is found that using innovative search strategies pair production of new coloured adjoint fermions producing a pure six-jet final state can be detected up to a mass of about 650-700 GeV with 10 fb-1 of integrated luminosity.