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In view of the recent start of the NA62 experiment at CERN that is expectedto 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 StandardModel (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 perturbativeQCD and electroweak corrections in both decays are under full control, thedominant uncertainties within the SM presently originate from the CKMparameters $V_{cb}$, $V_{ub}$ and $\gamma$. We show this dependence with thehelp of analytic expressions as well as accurate interpolating formulae.Unfortunately a clarification of the discrepancies between inclusive andexclusive determinations of $V_{cb}$ and $V_{ub}$ from tree-level decays willlikely require results from the Belle II experiment available at the end ofthis decade. Thus we investigate whether higher precision on both branchingratios is achievable by determining $V_{cb}$, $V_{ub}$ and $\gamma$ by means ofother observables that are already precisely measured. In this context$\varepsilon_K$ and $\Delta M_{s,d}$, together with the expected progress inQCD 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 ismore 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 isonly very weakly dependent on other CKM parameters. Finally, we also update theratio $\varepsilon'/\varepsilon$ in the SM and present its correlation with$K_L\to\pi^0\nu\bar\nu$.

$K^+\to\pi^+\nu\bar\nu$ and $K_L\to\pi^0\nu\bar\nu$ in the Standard Model: Status and Perspectives