Polar ring galaxies, where matter is in equilibrium in perpendicular
orbits around spiral galaxies, are ideal objects to probe the 3D shapes
of dark matter halos. The conditions to constrain the halos are that the
perpendicular system does not strongly perturb the host galaxy, or that
it is possible to derive back its initial shape, knowing the formation
scenario of the polar ring. The formation mechanisms are reviewed:
mergers, tidal accretion, or gas accretion from cosmic filaments.
The Tully-Fisher diagram for polar rings reveals that the velocity
in the polar plane is higher than in the host plane, which can
only be explained if the dark matter is oblate and flattened
along the polar plane. Only a few individual systems have
been studied in details, and 3D shapes of their haloes determined
by several methods. The high frequency of warps could be explained
by spontaneous bending instability, if the disks are sufficiently
self-gravitating, which can put constraints on the dark matter flattening.