Supersymmetry (SUSY) is a theoretical framework that pairs each fermion with a boson and vice versa, offering a solution to the hierarchy problem and providing a pathway to unify forces. It predicts a light Higgs boson and could link collider physics with cosmology. The LHC and ILC are key for discovering SUSY, with the LHC capable of detecting SUSY particles in cascade decays, while the ILC can measure them directly. The parameter space of SUSY is complex, requiring advanced tools for analysis. The minimal supersymmetric standard model (MSSM) has around 120 parameters, but constraints reduce this to 19. The SPS1a model is a typical case, with heavy squarks and gluinos, and the lightest Higgs boson near the LEP limit. Determining SUSY parameters involves Bayesian and frequentist methods, with the inclusion of theory and experimental errors improving precision. The MSSM allows extrapolation to high scales, providing insights into grand unification. The NMSSM extends the Higgs sector, while models like the cNMSSM reduce parameters. The LHC could detect the stau as the next-to-lightest supersymmetric particle (NLSP), with unique signatures. The Higgs couplings to b quarks and W bosons are critical, with new analysis techniques improving sensitivity. The LHC's potential for discovering sgluons is significant, with large cross sections. The precision of SUSY parameter determination at the LHC and ILC could rival that of WMAP and Planck. Supersymmetry remains a compelling candidate for new physics at the TeV scale, with the LHC ready for challenging scenarios. Future studies will explore SUSY's implications for dark matter and cosmology.Supersymmetry (SUSY) is a theoretical framework that pairs each fermion with a boson and vice versa, offering a solution to the hierarchy problem and providing a pathway to unify forces. It predicts a light Higgs boson and could link collider physics with cosmology. The LHC and ILC are key for discovering SUSY, with the LHC capable of detecting SUSY particles in cascade decays, while the ILC can measure them directly. The parameter space of SUSY is complex, requiring advanced tools for analysis. The minimal supersymmetric standard model (MSSM) has around 120 parameters, but constraints reduce this to 19. The SPS1a model is a typical case, with heavy squarks and gluinos, and the lightest Higgs boson near the LEP limit. Determining SUSY parameters involves Bayesian and frequentist methods, with the inclusion of theory and experimental errors improving precision. The MSSM allows extrapolation to high scales, providing insights into grand unification. The NMSSM extends the Higgs sector, while models like the cNMSSM reduce parameters. The LHC could detect the stau as the next-to-lightest supersymmetric particle (NLSP), with unique signatures. The Higgs couplings to b quarks and W bosons are critical, with new analysis techniques improving sensitivity. The LHC's potential for discovering sgluons is significant, with large cross sections. The precision of SUSY parameter determination at the LHC and ILC could rival that of WMAP and Planck. Supersymmetry remains a compelling candidate for new physics at the TeV scale, with the LHC ready for challenging scenarios. Future studies will explore SUSY's implications for dark matter and cosmology.