Abstract We present Keck/DEIMOS spectroscopy of the first complete sample of ultradiffuse 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 2.5σ 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 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.