This paper provides a comprehensive analysis of the constraints on gluino- and photino-mediated SUSY contributions to flavor-changing neutral currents (FCNC) and CP violation. The authors use the mass insertion method, a model-independent approach, to parameterize these contributions and apply it to various extensions of the Minimal Supersymmetric Standard Model (MSSM). They clarify controversial points in the literature, particularly concerning the CP violating parameter \(\varepsilon'\), and provide a more detailed analysis of the constraints. The paper also explores the implications of these constraints in SUSY-GUTs and effective supergravities with non-universal soft SUSY breaking terms. The authors compare their results with previous analyses and discuss the applicability and implementation of the mass insertion approach in realistic SUSY models. The analysis covers both \(\Delta F = 2\) and \(\Delta F = 1\) processes, including limits on sfermion masses, CP-violating parameters, and flavor-diagonal mass insertions. The paper concludes with a discussion on QCD corrections and their impact on the constraints, as well as a comparison of the mass insertion approach with exact results obtained in the physical basis for fermions and sfermions.This paper provides a comprehensive analysis of the constraints on gluino- and photino-mediated SUSY contributions to flavor-changing neutral currents (FCNC) and CP violation. The authors use the mass insertion method, a model-independent approach, to parameterize these contributions and apply it to various extensions of the Minimal Supersymmetric Standard Model (MSSM). They clarify controversial points in the literature, particularly concerning the CP violating parameter \(\varepsilon'\), and provide a more detailed analysis of the constraints. The paper also explores the implications of these constraints in SUSY-GUTs and effective supergravities with non-universal soft SUSY breaking terms. The authors compare their results with previous analyses and discuss the applicability and implementation of the mass insertion approach in realistic SUSY models. The analysis covers both \(\Delta F = 2\) and \(\Delta F = 1\) processes, including limits on sfermion masses, CP-violating parameters, and flavor-diagonal mass insertions. The paper concludes with a discussion on QCD corrections and their impact on the constraints, as well as a comparison of the mass insertion approach with exact results obtained in the physical basis for fermions and sfermions.