  Many independent high-resolution simulations of structure formation in cold
dark matter models show that galactic halos should have singular core profiles.
This is in stark contrast with observations of both low- and high-surface
brightness galaxies, which indicate that the dark matter has almost constant
density in the central parts of halos. Basically there are three possible
avenues to a solution to the problem, which we discuss in turn. Observations of
halo profiles could be more uncertain than previously thought, and higher
resolution observations could reveal that spirals do have a singular core
feature. The highest resolution simulations do not include a baryonic
component, and it is conceivable that violent star formation processes and
similar phenomena can destroy the singular dark matter core and lead to an
almost constant density core profile. Finally, we discuss in more detail the
intriguing possibility that the discrepancy hints at some new exotic physics of
the dark matter. Warm dark matter and self-interacting dark matter are two of
the most promising candidates.
