  We present Keck/DEIMOS spectroscopy of the first complete sample of
ultra-diffuse galaxies (UDGs) in the Virgo cluster. We select all UDGs in Virgo
that contain at least 10 globular cluster (GC) candidates and are more than
$2.5\sigma$ outliers in scaling relations of size, surface brightness, and
luminosity (a total of 10 UDGs). We use the radial velocity of their GC
satellites to measure the velocity dispersion of each UDG. We find a mixed bag
of galaxies: from one UDG that shows no signs of dark matter, to UDGs that
follow the luminosity-dispersion relation of early-type galaxies, to the most
extreme examples of heavily dark matter dominated galaxies that break
well-known scaling relations such as the luminosity-dispersion or the U-shaped
total mass-to-light ratio relations. This is indicative of a number of
mechanisms at play forming these peculiar galaxies. Some of them may be the
most extended version of dwarf galaxies, while others are so extreme that they
seem to populate dark matter halos consistent with that of the Milky-Way or
even larger. Even though Milky-Way stars and other GC interlopers contaminating
our sample of GCs cannot be fully ruled-out, our assessment of this potential
problem and simulations indicate that the probability is low and, if present,
unlikely to be enough to explain the extreme dispersions measured. Further
confirmation from stellar kinematics studies in these UDGs would be desirable.
The lack of such extreme objects in any of the state-of-the-art simulations,
opens an exciting avenue of new physics shaping these galaxies.
