  We consider fermionic polar molecules in a bilayer geometry where they are
oriented perpendicularly to the layers, which permits both low inelastic losses
and superfluid pairing. The dipole-dipole interaction between molecules of
different layers leads to the emergence of interlayer superfluids. The
superfluid regimes range from BCS-like fermionic superfluidity with a high
$T_c$ to Bose-Einstein (quasi-)condensation of interlayer dimers, thus
exhibiting a peculiar BCS-BEC crossover. We show that one can cover the entire
crossover regime under current experimental conditions.
