  The viscosity of strongly interacting systems is a topic of great interest in
diverse fields.
  We focus here on the bulk and shear viscosities of \emph{non-relativistic}
quantum fluids, with particular emphasis on strongly interacting ultracold
Fermi gases. We use Kubo formulas for the bulk and shear viscosity spectral
functions, $\zeta(\omega)$ and $\eta(\omega)$ respectively, to derive exact,
non-perturbative results. Our results include: a microscopic connection between
the shear viscosity $\eta$ and the normal fluid density $\rho_n$; sum rules for
$\zeta(\omega)$ and $\eta(\omega)$ and their evolution through the BCS-BEC
crossover; universal high-frequency tails for $\eta(\omega)$ and the dynamic
structure factor $S({\bf q}, \omega)$. We use our sum rules to show that, at
unitarity, $\zeta(\omega)$ is identically zero and thus relate $\eta(\omega)$
to density-density correlations. We predict that frequency-dependent shear
viscosity $\eta(\omega)$ of the unitary Fermi gas can be experimentally
measured using Bragg spectroscopy.
