**Summary:** This review discusses the QCD corrections to weak decays beyond the leading logarithmic approximation, including particle-antiparticle mixing and rare and CP-violating decays. The authors present the basic formalism for these calculations, focusing on effective Hamiltonians for various decays where next-to-leading corrections are known. They discuss the phenomenological implications, updating parameter values and incorporating new information on the top quark mass. A central issue is the theoretical uncertainty due to renormalization scale ambiguities, which are significantly reduced by including next-to-leading order corrections. The impact of these improvements on the determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is illustrated in various cases. The review covers the Standard Electroweak Model, basic formalism for QCD effects in weak decays, and the renormalization group. It discusses the operator product expansion, Wilson coefficients, and the renormalization group evolution. The effective Hamiltonians for different decays, such as $ \Delta F = 1 $ and $ \Delta B = 1 $, are analyzed, including the inclusion of QCD and electroweak penguin operators. The review also addresses rare $ K $- and $ B $-decays, $ K_L \rightarrow \pi^0 e^+ e^- $, $ B \rightarrow X_s \gamma $, and $ B \rightarrow X_s e^+ e^- $, discussing their effective Hamiltonians and numerical results. The unitarity triangle and CP violation are also discussed, with a focus on the $ \varepsilon'/\varepsilon $ parameter and the $ \Delta I = 1/2 $ rule. The review concludes with a summary of results and an outlook on future developments in the field.**Summary:** This review discusses the QCD corrections to weak decays beyond the leading logarithmic approximation, including particle-antiparticle mixing and rare and CP-violating decays. The authors present the basic formalism for these calculations, focusing on effective Hamiltonians for various decays where next-to-leading corrections are known. They discuss the phenomenological implications, updating parameter values and incorporating new information on the top quark mass. A central issue is the theoretical uncertainty due to renormalization scale ambiguities, which are significantly reduced by including next-to-leading order corrections. The impact of these improvements on the determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is illustrated in various cases. The review covers the Standard Electroweak Model, basic formalism for QCD effects in weak decays, and the renormalization group. It discusses the operator product expansion, Wilson coefficients, and the renormalization group evolution. The effective Hamiltonians for different decays, such as $ \Delta F = 1 $ and $ \Delta B = 1 $, are analyzed, including the inclusion of QCD and electroweak penguin operators. The review also addresses rare $ K $- and $ B $-decays, $ K_L \rightarrow \pi^0 e^+ e^- $, $ B \rightarrow X_s \gamma $, and $ B \rightarrow X_s e^+ e^- $, discussing their effective Hamiltonians and numerical results. The unitarity triangle and CP violation are also discussed, with a focus on the $ \varepsilon'/\varepsilon $ parameter and the $ \Delta I = 1/2 $ rule. The review concludes with a summary of results and an outlook on future developments in the field.