  We review the current status of theoretical predictions for mixing quantities
and lifetimes in the $B$-sector. In particular, due to the first non-zero
measurement of the decay rate difference in the neutral $B_s$-system, $\Delta
\Gamma_s/ \Gamma_s = 17.6 % \pm 2.9 %$ by the LHCb collaboration and very
precise data for $\tau_{B_s}$ from TeVatron and LHCb our theoretical tools can
now be rigorously tested and it turns out that the Heavy Quark Expansion works
in the $B$-system to an accuracy of at least 30% for quantities like
$\Gamma_{12}$, which is most sensitive to hypothetical violations of quark
hadron duality. This issue that gave rise in the past to numerous theoretical
papers, has now been settled experimentally. Further data will even allow to
shrink this bound. For total inclusive quantities like lifetimes the compliance
is even more astonishing: $\tau_{B_s}^{\rm LHCb}/ \tau_{B_d}^{\rm HFAG} = 1.001
\pm 0.014$ is in perfect agreement with the theory expectation of
$\tau_{B_s}/\tau_{B_d} = 0.996 ... 1.000$. Despite the fact that the new data
show no deviations from the standard model expectations, there is still some
sizable room for new physics effects. Model-independent search strategies for
these effects are presented with an emphasis on the interconnection with many
different observables that have to be taken into account. In that respect a
special emphasis is given to the large value of the di-muon asymmetry measured
by the D0 collaboration.
