Real relativistic fluids in heavy ion collisions

The theory of real relativistic fluids is in the rather unique situation that there is a natural relativistic extension of the nonrelativistic theory, but it is physically untenable. On the other hand, mounting evidence that matter created in relativistic heavy ion collisions behaves as a relativistic fluid with small but finite viscosity has given the quest for an alternative a definite goal. We shall review different approaches to relativistic real fluids, their link to relativistic kinetic theory, and their application to the analysis of heavy ion collisions