  The steady compressible Navier--Stokes--Fourier system is considered, with
either Dirichlet or Navier boundary conditions for the velocity and the heat
flux on the boundary proportional to the difference of the temperature inside
and outside. In dependence on several parameters, i.e. the adiabatic constant
$\gamma$ appearing in the pressure law $p(\vr,\vt) \sim \vr^\gamma + \vr \vt$
and the growth exponent in the heat conductivity, i.e. $\kappa(\vt) \sim (1+
\vt^m)$, and without any restriction on the size of the data, the main ideas of
the construction of weak and variational entropy solutions for the
three-dimensional flows with temperature dependent viscosity coefficients are
explained. Further, the case when it is possible to prove existence of
solutions with bounded density is reviewed. The main changes in the
construction of solutions for the two-dimensional flows are mentioned and
finally, results for more complex systems are reviewed, where the steady
compressible Navier--Stokes--Fourier equations play an important role.
