  In the heavy-quark limit, the hadronic matrix elements entering nonleptonic
$B$-meson decays into two light mesons can be calculated from first principles
including ``nonfactorizable'' strong-interaction corrections. The $B\to\pi
K,\pi\pi$ decay amplitudes are computed including electroweak penguin
contributions, SU(3) violation in the light-cone distribution amplitudes, and
an estimate of power corrections from chirally-enhanced terms and annihilation
graphs. The results are then used to reduce the theoretical uncertainties in
determinations of the weak phases $\gamma$ and $\alpha$. In that way, new
constraints in the $(\bar\rho,\bar\eta)$ plane are derived. Predictions for the
$B\to\pi K, \pi\pi$ branching ratios and CP asymmetries are also presented. A
good global fit to the (in part preliminary) experimental data on the branching
fractions is obtained without taking recourse to phenomenological models.
