We analyse the present experimental evidence for a complex CKM matrix, even allowing for New Physics contributions to ϵK, aJ/ΨKS%, ΔMBd, ΔMBs, and the ΔI=1/2 piece of and B→ρπ. We emphasize the crucial r\^{o}le played by the angle γ in both providing irrefutable evidence for a 3×3 complex CKM matrix and placing constraints on the size of NP contributions. It is shown that even if one allows for New Physics a real CKM matrix is excluded at a 99.92% C.L., and the probability for the phase γ to be in the interval [−170∘:−10∘]∪[10∘:170∘] is 99.7%. Large value of the phase χ, e.g. of order λ, is only possible in models where the unitarity of the 3×3 Cabibbo-Kobayashi-Maskawa matrix is violated through the introduction of extra Q=2/3 quarks. We study the allowed range for χ and the effect of a large χ on various low-energy observables, such as CP asymmetries in B meson decays. We also discuss the correlated effects which would be observable at high energy colliders, like decays t→cZ, etc..