As a well-established theory the Standard Model has been serving the physicists for decades. This theory is by no means a complete one because of a number of problems not yet explained, among which the hierarchy problem is the most notorious one. Supersymmetry is a major candidate to solve the hierarchy problem. Theories based on supersymmetry together with other ingredients can be plausible solutions to dark matter, grand unification, neutrino oscillation, CP violation etc.

Three different supersymmetric models will be presented after a brief description of the Standard Model and the Minimal Supersymmetric Standard Model. First a model of mixed anomaly and gauge mediation is presented, which gives a natural solution to the SUSY flavor problem with a conventional dark matter candidate, the LSP. The model also include a natural relaxation mechanism that generates the Bμ term of the right size. The second model has particles with TeV mass and strong self-interactions, which generically have the right annihilation cross section to explain an observed excess of cosmic electrons and positrons. The relic abundance of the dark matter is related to the matter-antimatter asymmetry of the observed universe. The last one is a supersymmetric grand unification model based on SO(10) group with S4 flavor symmetry. This model fits all the masses and mixing of the quarks and leptons and predicts a testable sin &thetas; ₁₃. Leptonic CP violation is also studied.