This paper presents a general analysis of extensions of the Standard Model (SM) that satisfy the criterion of Minimal Flavour Violation (MFV). The authors define a low-energy effective theory containing SM fields, with one or two Higgs doublets, where the only source of SU(3)^5 flavour symmetry breaking is the background values of fields transforming under the flavour group as ordinary Yukawa couplings. They analyze current bounds on the effective scale of dimension-six operators, which range from 1 to 10 TeV, with the most stringent constraints coming from the B → Xsγ decay. In this class of theories, predictions for FCNC processes in B physics can be related to those in K physics. The authors compare the sensitivity of various experimental searches in probing the MFV hypothesis. Within the two-Higgs-doublet scenario, they develop a general procedure to obtain all tanβ-enhanced Higgs-mediated FCNC amplitudes, discussing their impact in B → ℓ+ℓ−, ΔMB, and B → Xsγ. As a byproduct, they derive some two-loop tanβ-enhanced supersymmetric contributions to B → Xsγ previously unknown. The paper discusses the implications of MFV in the context of supersymmetry, where the scalar-mass soft terms are universal and the trilinear soft terms are proportional to Yukawa couplings. The authors show how the MFV hypothesis can be consistently defined independently of the structure of the new-physics model, describe the generic form of an effective theory obeying this hypothesis, and derive the present constraints on the characteristic scale Λ. They find that the constraints vary from 1 TeV to about 10 TeV, with the strongest bound coming from B → Xsγ. The paper also discusses the implications of MFV in models with non-perturbative interactions at energies Λ, such as in scenarios with low-energy quantum-gravity scale. The authors show how the effective theory approach provides a simple systematic tool to identify tanβ-enhanced Higgs-mediated FCNC amplitudes and, using it, identify a contribution to B → Xsγ which so far has not been discussed in the literature. The paper concludes that the description of flavour violations in terms of an effective theory is a useful tool to analyze future data on B and K mesons. When deviations from the SM predictions are observed, the comparison among various processes will indicate if they can be described in the general framework of MFV, or if they require new flavour structures. This will be a crucial hint to identify the correct theory valid above the cut-off scale Λ.This paper presents a general analysis of extensions of the Standard Model (SM) that satisfy the criterion of Minimal Flavour Violation (MFV). The authors define a low-energy effective theory containing SM fields, with one or two Higgs doublets, where the only source of SU(3)^5 flavour symmetry breaking is the background values of fields transforming under the flavour group as ordinary Yukawa couplings. They analyze current bounds on the effective scale of dimension-six operators, which range from 1 to 10 TeV, with the most stringent constraints coming from the B → Xsγ decay. In this class of theories, predictions for FCNC processes in B physics can be related to those in K physics. The authors compare the sensitivity of various experimental searches in probing the MFV hypothesis. Within the two-Higgs-doublet scenario, they develop a general procedure to obtain all tanβ-enhanced Higgs-mediated FCNC amplitudes, discussing their impact in B → ℓ+ℓ−, ΔMB, and B → Xsγ. As a byproduct, they derive some two-loop tanβ-enhanced supersymmetric contributions to B → Xsγ previously unknown. The paper discusses the implications of MFV in the context of supersymmetry, where the scalar-mass soft terms are universal and the trilinear soft terms are proportional to Yukawa couplings. The authors show how the MFV hypothesis can be consistently defined independently of the structure of the new-physics model, describe the generic form of an effective theory obeying this hypothesis, and derive the present constraints on the characteristic scale Λ. They find that the constraints vary from 1 TeV to about 10 TeV, with the strongest bound coming from B → Xsγ. The paper also discusses the implications of MFV in models with non-perturbative interactions at energies Λ, such as in scenarios with low-energy quantum-gravity scale. The authors show how the effective theory approach provides a simple systematic tool to identify tanβ-enhanced Higgs-mediated FCNC amplitudes and, using it, identify a contribution to B → Xsγ which so far has not been discussed in the literature. The paper concludes that the description of flavour violations in terms of an effective theory is a useful tool to analyze future data on B and K mesons. When deviations from the SM predictions are observed, the comparison among various processes will indicate if they can be described in the general framework of MFV, or if they require new flavour structures. This will be a crucial hint to identify the correct theory valid above the cut-off scale Λ.