  We study varying forms of viscous dark matter and try to address the
intriguing tensions of the standard model of cosmology with recent cosmological
data, including the Hubble and $S_8$ tensions. We note that by assuming the
dark matter viscosity depends on the Hubble parameter, dark matter density, or
both, one can improve the statistics. Although the models tend to aggravate the
Hubble tension a bit, they tend to reduce the $S_8$ tension, even in comparison
with the constant viscosity case. Since similar to viscosity massive neutrinos
suppress the power spectrum of matter on small length scales, considering them
along with the viscous dark matter, we find that the neutrino mass range is
tightened.
