  The interaction between a supersonic stellar wind and a (super-)sonic
interstellar wind has recently been viewed with new interest. We here first
give an overview of the modeling, which includes the heliosphere as an example
of a special astrosphere. Then we concentrate on the shock structures of fluid
models, especially of hydrodynamic (HD) models. More involved models taking
into account radiation transfer and magnetic fields are briefly sketched. Even
the relatively simple HD models show a rich shock structure, which might be
observable in some objects. We employ a single fluid model to study these
complex shock structures, and compare the results obtained including heating
and cooling with results obtained without these effects. Furthermore, we show
that in the hypersonic case valuable information of the shock structure can be
obtained from the Rankine-Hugoniot equations. We solved the Euler equations for
the single fluid case and also for a case including cooling and heating. We
also discuss the analytical Rankine-Hugoniot relations and their relevance to
observations. We show that the only obtainable length scale is the termination
shock distance. Moreover, the so-called thin shell approximation is usually not
valid. We present the shock structure in the model that includes heating and
cooling, which differs remarkably from that of a single fluid scenario in the
region of the shocked interstellar medium. We find that the heating and cooling
is mainly important in this region and is negligible in the regions dominated
by the stellar wind beyond an inner boundary.
