Waiting for precise measurements of K+→π+ν(ν)over-bar and KL→π0ν(ν)over-bar

In view of future plans for accurate measurements of the theoretically clean branching ratios Br(K+->pi(+)nu(nu) over bar) and Br(K-L ->pi(0)nu(nu) over bar), which should occur in the next decade, the relevant formulas for quantities of interest are collected and their theoretical and parametric uncertainties are analyzed. In addition to the angle beta in the unitarity triangle (UT), the angle gamma can also be determined from these decays with respectable precision and in this context the importance of the recent NNLO QCD calculation on the charm contribution to K+->pi(+)nu(nu) over bar and of the improved estimate on the long-distance contribution by means of chiral perturbation theory are presented. In addition to known expressions, several new ones that should allow transparent tests of the standard model (SM) and of its extensions are presented. While the review is centered around the SM, models with minimal flavor violation and scenarios with new complex phases in decay amplitudes and meson mixing are also discussed. A review of existing results within specific extensions of the SM, in particular the littlest Higgs model with T-parity, Z(') models, the MSSM, and a model with one universal extra dimension are given. A new golden relation between B and K systems is derived that involves (beta,gamma) and Br(K-L ->pi(0)nu(nu) over bar), and the virtues of (R-t,beta), (R-b,gamma), (beta,gamma), and ((eta) over bar,gamma) strategies for the UT in the context of K ->pi nu(nu) over bar decays with the goal of testing the SM and its extensions are investigated.