  We compute the amplitudes for the two-body decay of $B$ mesons into
longitudinally polarized light vector mesons at next-to-leading order in QCD.
We give the explicit expressions in QCD factorization for all 34 transitions of
a heavy-light $B$ meson into a pair of longitudinal vector mesons $\rho$,
$\omega$, $\phi$, $K^*$ within the Standard Model. Decay rates and CP
asymmetries are discussed in detail and compared with available data.
Exploiting the fact that QCD penguins are systematically smaller for vector
mesons in comparison to pseudoscalars in the final state, we investigate
several methods to achieve high-precision determinations of CKM parameters and
New Physics tests. We propose a method to use V-spin symmetry and data on $\bar
B_d\to\bar K^{*0}_L K^{*0}_L$ to constrain the penguin contribution in $\bar
B_d\to\rho^+_L\rho^-_L$. CP violation in the latter decay together with a
measurement of $\sin 2\beta$ determines the unitarity triangle with high
accuracy. We show that CP violation in $\bar B_d\to\rho^+_L\rho^-_L$ and $\bar
B_d\to\psi K_S$ alone implies $|V_{ub}|=(3.54\pm 0.17)\cdot 10^{-3}$, presently
the most accurate determination of this quantity.
