After briefly describing the Standard Model and its hierarchy problem, I focus on supersymmetry as an elegant solution to the hierarchy problem and describe the Minimal Supersymmetric Standard Model. I then present two well-motivated models of supersymmetry-breaking based on the ideas of gauge- and anomaly-mediated supersymmetry-breaking. These two models are constructed to alleviate the little hierarchy problem of the Minimal Supersymmetric Standard Model, and can naturally offer distinct collider signatures. I describe typical spectra of these two models and discuss their collider signatures at the Large Hadron Collider.

I also present a model based on universal extra dimensions that solves both the problems of proton decay and neutrino masses in the minimal framework. The model offers an interesting dark matter candidate as an admixture of Kaluza-Klein modes, and I analysis the range in parameter space that may give the observed relic density of dark matter and the prospects of direct detection within the viable parameter space.