  We calculate the complete NNLO QCD corrections to the charm contribution of
the rare decay K+ -> pi+ nu nu-bar. We encounter several new features, which
were absent in lower orders. We discuss them in detail and present the results
for the 2-loop matching conditions of the Wilson coefficients, the 3-loop
anomalous dimensions, and the 2-loop matrix elements of the relevant operators
that enter the NNLO renormalization group analysis of the Z-penguin and the
electroweak box contribution. The inclusion of the NNLO QCD corrections leads
to a significant reduction of the theoretical uncertainty from 9.8% down to
2.4% in the relevant parameter Pc, implying the leftover scale uncertainties in
BR(K+ -> pi+ nu nu-bar) and in the determination of |V_td|, sin(2 beta), and
gamma from the K -> pi nu nu system to be 1.3%, 1.0%, 0.006, and 1.2 degrees,
respectively. For the charm quark MSbar mass mc=(1.30+-0.05) GeV and |V_us|=
0.2248 the NLO value Pc=0.37+-0.06 is modified to Pc=0.38+-0.04 at the NNLO
level with the latter error fully dominated by the uncertainty in mc. We
present tables for Pc as a function of mc and alphas(MZ) and a very accurate
analytic formula that summarizes these two dependences as well as the dominant
theoretical uncertainties. Adding the recently calculated long-distance
contributions we find BR(K+ -> pi+ nu nu-bar)=(8.0+-1.1)*10^-11 with the
present uncertainties in mc and the Cabibbo-Kobayashi-Maskawa elements being
the dominant individual sources in the quoted error. We also emphasize that
improved calculations of the long-distance contributions to K+ -> pi+ nu nu-bar
and of the isospin breaking corrections in the evaluation of the weak current
matrix elements from K+ -> pi0 e+ nu would be valuable in order to increase the
potential of the two golden K -> pi nu nu decays in the search for new physics.
