Dissipative fluids appear in many problems in physics and astrophysics, from heavy ion collision to accretion discs. But the usual Navier-Stokes theory does not have a direct generalization to relativity, the simplest attempts give ill posed problems.
We shall introduce well behaved theories and focus attention to the conformally invariant class. We shall show that class depends on just two main constant parameters and that they can be chosen so that the resulting equations are symmetric hyperbolic.