  We explore the glassy dynamics of soft colloids using microgels and charged
particles interacting by steric and screened Coulomb interactions,
respectively. In the supercooled regime, the structural relaxation time
$\tau_\alpha$ of both systems grows steeply with volume fraction, reminiscent
of the behavior of colloidal hard spheres. Computer simulations confirm that
the growth of $\tau_\alpha$ on approaching the glass transition is independent
of particle softness. By contrast, softness becomes relevant at very large
packing fractions when the system falls out of equilibrium. In this
non-equilibrium regime, $\tau_\alpha$ depends surprisingly weakly on packing
fraction and time correlation functions exhibit a compressed exponential decay
consistent with stress-driven relaxation. The transition to this novel regime
coincides with the onset of an anomalous decrease of local order with
increasing density typical of ultrasoft systems. We propose that these peculiar
dynamics results from the combination of the non-equilibrium aging dynamics
expected in the glassy state and the tendency of colloids interacting through
soft potentials to refluidize at high packing fractions.
