  The measured B -> pi pi, pi K branching ratios exhibit puzzling patterns. We
point out that the B -> pi pi hierarchy can be nicely accommodated in the
Standard Model (SM) through non-factorizable hadronic interference effects,
whereas the B -> pi K system may indicate new physics (NP) in the electroweak
(EW) penguin sector. Using the B -> pi pi data and the SU(3) flavour symmetry,
we may fix the hadronic B -> pi K parameters, which allows us to show that any
currently observed feature of the B -> pi K system can be easily explained
through enhanced EW penguins with a large CP-violating NP phase. Restricting
ourselves to a specific scenario, where NP enters only through Z^0 penguins, we
derive links to rare K and B decays, where an enhancement of the K_L-> pi^0 nu
nu_bar rate by one order of magnitude, with BR(K_L -> pi^0 nu nu_bar) > BR(K^+
-> pi^+ nu nu_bar), BR(K_L -> pi^0 e^+ e^-)=O(10^{-10}), (\sin2\beta)_{pi nu
nu_bar}<0, and a large forward-backward CP asymmetry in B_d -> K* mu^+ mu^-,
are the most spectacular effects. We address also other rare K and B decays,
epsilon'/epsilon and B_d -> phi K_S.
