This review discusses the QCD corrections to weak decays beyond the leading logarithmic approximation, including particle-antiparticle mixing and rare and CP-violating decays. It begins by presenting the basic formalism for these calculations, which involves the operator product expansion (OPE) and the renormalization group (RG) equations. The effective Hamiltonians for various decays, such as $K \to \pi \pi$, $K_L \to \pi^0 e^+ e^-$, $B \to X_s \gamma$, and $B \to X_s e^+ e^-$, are derived and discussed in detail. The impact of these corrections on the determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is illustrated, and the theoretical uncertainties related to renormalization scale ambiguities are addressed. The review also updates the values of various parameters, incorporating new information on the top quark mass. The phenomenological implications of these calculations are presented, including the impact on the unitarity triangle and the determination of CP violation parameters like $\varepsilon'/\varepsilon$. The review concludes with a summary of the results and an outlook on future research directions.This review discusses the QCD corrections to weak decays beyond the leading logarithmic approximation, including particle-antiparticle mixing and rare and CP-violating decays. It begins by presenting the basic formalism for these calculations, which involves the operator product expansion (OPE) and the renormalization group (RG) equations. The effective Hamiltonians for various decays, such as $K \to \pi \pi$, $K_L \to \pi^0 e^+ e^-$, $B \to X_s \gamma$, and $B \to X_s e^+ e^-$, are derived and discussed in detail. The impact of these corrections on the determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is illustrated, and the theoretical uncertainties related to renormalization scale ambiguities are addressed. The review also updates the values of various parameters, incorporating new information on the top quark mass. The phenomenological implications of these calculations are presented, including the impact on the unitarity triangle and the determination of CP violation parameters like $\varepsilon'/\varepsilon$. The review concludes with a summary of the results and an outlook on future research directions.