  In view of the recent start of the NA62 experiment at CERN that is expected
to measure the $K^+\to\pi^+\nu\bar\nu$ branching ratio with a precision of 10%,
we summarise the present status of this promising decay within the Standard
Model (SM). We do likewise for the closely related $K_L\to\pi^0\nu\bar\nu$,
which will be measured by the KOTO experiment around 2020. As the perturbative
QCD and electroweak corrections in both decays are under full control, the
dominant uncertainties within the SM presently originate from the CKM
parameters $V_{cb}$, $V_{ub}$ and $\gamma$. We show this dependence with the
help of analytic expressions as well as accurate interpolating formulae.
Unfortunately a clarification of the discrepancies between inclusive and
exclusive determinations of $V_{cb}$ and $V_{ub}$ from tree-level decays will
likely require results from the Belle II experiment available at the end of
this decade. Thus we investigate whether higher precision on both branching
ratios is achievable by determining $V_{cb}$, $V_{ub}$ and $\gamma$ by means of
other observables that are already precisely measured. In this context
$\varepsilon_K$ and $\Delta M_{s,d}$, together with the expected progress in
QCD lattice calculations will play a prominent role. We find
$\mathcal{B}(K^+\to\pi^+\nu\bar\nu) = (9.11\pm 0.72) \times 10^{-11}$ and
$\mathcal{B}(K_L\to\pi^0\nu\bar\nu) = (3.00\pm 0.30) \times 10^{-11}$, which is
more precise than using averages of the present tree-level values of $V_{cb}$,
$V_{ub}$ and $\gamma$. Furthermore, we point out the correlation between
$\mathcal{B}(K^+\to\pi^+\nu\bar\nu)$,
$\overline{\mathcal{B}}(B_s\to\mu^+\mu^-)$ and $\gamma$ within the SM, that is
only very weakly dependent on other CKM parameters. Finally, we also update the
ratio $\varepsilon'/\varepsilon$ in the SM and present its correlation with
$K_L\to\pi^0\nu\bar\nu$.
