  We report on recent progress in studying two aspects of $B$ physics, in which
penguin amplitudes play an important role: (1) Bounds on penguin pollution in
$B^0(t) \to \pi^+\pi^-$ constraining CKM parameters, and a lower bound on $B^0
\to \pi^0\pi^0$ improving precision in $\sin 2\alpha$. (2) A suggestion for
measuring the photon polarization in electroweak penguin decay, $B \to
K_1(1400)\gamma$, providing a precision test of the Standard Model and a probe
for new physics.
