  The recent results by the Fermilab Lattice and MILC collaborations on the
hadronic matrix elements entering $B_{d,s}-\bar B_{d,s}$ mixing show a
significant tension of the measured values of the mass differences $\Delta
M_{d,s}$ with their SM predictions. We review the implications of these results
in the context of Constrained Minimal Flavour Violation models. In these
models, the CKM elements $\gamma$ and $|V_{ub}|/|V_{cb}|$ can be determined
from $B_{d,s}-\bar B_{d,s}$ mixing observables, yielding a prediction for
$\gamma$ below its tree-level value. Determining subsequently $|V_{cb}|$ from
the measured value of either $\Delta M_s$ or $\varepsilon_K$ gives inconsistent
results, with the tension being smallest in the Standard Model limit. This
tension can be resolved if the flavour universality of new contributions to
$\Delta F = 2$ observables is broken. We briefly discuss the case of $U(2)^3$
flavour models as an illustrative example.
