  Gas-rich circumstellar disks are the cradles of planet formation. As such,
their evolution will strongly influence the resulting planet population. In the
ESO DESTINYS large program, we study these disks within the first 10 Myr of
their development with near-infrared scattered light imaging. Here we present
VLT/SPHERE polarimetric observations of the nearby class II system SU Aur in
which we resolve the disk down to scales of ~7 au. In addition to the new
SPHERE observations, we utilize VLT/NACO, HST/STIS and ALMA archival data. The
new SPHERE data show the disk around SU Aur and extended dust structures in
unprecedented detail. We resolve several dust tails connected to the Keplerian
disk. By comparison with ALMA data, we show that these dust tails represent
material falling onto the disk. The disk itself shows an intricate spiral
structure and a shadow lane, cast by an inner, misaligned disk component. Our
observations suggest that SU Aur is undergoing late infall of material, which
can explain the observed disk structures. SU Aur is the clearest observational
example of this mechanism at work and demonstrates that late accretion events
can still occur in the class II phase, thereby significantly affecting the
evolution of circumstellar disks. Constraining the frequency of such events
with additional observations will help determine whether this process is
responsible for the spin-orbit misalignment in evolved exoplanet systems.
