  The LHCb collaboration has recently reported the first observation of CP
violation in the penguin-dominated $B^0_s\to K^-K^+$ decay and further new
measurements, indicating differences between the direct CP asymmetries of both
the $B^0_s\to K^-K^+$, $B^0_d\to\pi^-K^+$ and the $B^0_d\to \pi^-\pi^+$,
$B^0_s\to K^-\pi^+$ modes. We show that these puzzling differences can be
accommodated through sizeable penguin annihilation and exchange topologies in
the Standard Model, and constrain them. Utilising the $U$-spin symmetry, we
extract the angle $\gamma$ of the unitarity triangle from the CP asymmetries in
the $B^0_s\to K^-K^+$, $B^0_d\to \pi^-\pi^+$ system alone, finding
$\gamma=(65^{+11}_{-7})^\circ$, in perfect agreement with the determination
from tree-level $B\to DK$ decays. The $B^0_s$--$\bar B^0_s$ mixing phase
$\phi_s$ can be extracted from CP violation measurements in $B^0_s\to K^-K^+$
in a clean way. We present a new strategy and extract $\phi_s=-(3.6\pm
5.4)^\circ$. This result is in agreement with the determination from $B^0_s\to
J/\psi \phi$ decays. New CP-violating contributions would influence these
determinations differently. Hence it is interesting to keep monitoring both as
the experimental picture sharpens.
