  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
