  Based on recent HQET sum rule and lattice calculations we present updated
Standard Model predictions for the mass differences of neutral $B$ mesons:
$\Delta M_s^{\rm SM} = \left(18.4^{+0.7}_{-1.2} \right) \mbox{ps}^{-1}$ and
$\Delta M_d^{\rm SM} = \left(0.533^{+0.022}_{-0.036} \right) \mbox{ps}^{-1}$
and study their impact on new physics models that address the present hints of
anomalous data in $b \to s \ell \ell$ transitions. We also examine future
prospects of further reducing the theory uncertainties and discuss the
implications of a 2025 scenario with $\Delta M_s^\text{SM 2025} = \left(18.4
\pm 0.5\right) \mbox{ps}^{-1}$. In particular, the latter yields upper bounds
$M_{Z'}\lesssim 9~\text{TeV}$ and $M_{S_3}\lesssim 30~\text{TeV}$ for the
minimal $Z'$ and $S_3$ lepto-quark explanations of the $b \to s \ell \ell$
anomalies, respectively.
