  The recent observation of B_d -> pi^0 pi^0 at the B factories with a
surprisingly large branching ratio represents a challenge for theory, and
complements the amazingly small B_d -> pi^+ pi^- rate. We point out that all
puzzling B -> pi pi features can be accommodated in the Standard Model (SM)
through non-factorizable hadronic interference effects, extract the relevant
parameters, and predict the CP asymmetries of B_d -> pi^0 pi^0. Using then
SU(3) flavour-symmetry and plausible dynamical assumptions, we fix the hadronic
B -> pi K parameters through their B -> pi pi counterparts, and determine the
CKM angle gamma, with a result in remarkable accordance with the usual fits for
the unitarity triangle. We may then analyse the B -> pi K system in the SM,
where we find agreement with the experimental picture, with the exception of
those observables that are significantly affected by electroweak (EW) penguins,
thereby suggesting new physics (NP) in this sector. Indeed, a moderate
enhancement of these topologies and a large CP-violating NP phase allow us to
describe any currently observed feature of the B -> pi K modes, and to predict
the CP-violating B_d -> pi^0 K_S observables. If we then restrict ourselves to
a specific scenario where NP enters only through Z^0 penguins, we obtain a link
to rare K and B decays, where the most spectacular NP effects are 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) ~ 4 BR(K^+ -> pi^+ nu nu_bar), BR(K_L -> pi^0 e^+
e^-) = O(10^-10), (sin 2beta)_{pi nu nu_bar} < 0, and a large forward-backward
CP asymmetry in B_d -> K^* mu^+ mu^-. We address also epsilon'/epsilon and
other prominent decays, including B -> phi K and B -> J/psi K modes.
