  In view of the recent interest in reproducing holographically various
properties of conformal fluids, we review the issue of vorticity in the context
of AdS/CFT. Three-dimensional fluids with vorticity require four-dimensional
bulk geometries with either angular momentum or nut charge, whose boundary
geometries fall into the Papapetrou--Randers class. The boundary fluids emerge
in stationary non-dissipative kinematic configurations, which can be cyclonic
or vortex flows, evolving in compact or non-compact supports. A rich network of
Einstein's solutions arises, naturally connected with three-dimensional Bianchi
spaces. We use Fefferman--Graham expansion to handle holographic data from the
bulk and discuss the alternative for reversing the process and reconstruct the
exact bulk geometries.
