  We present the first to date high resolution calculations of the ISM down to
scales of 0.625 pc of the global and local ISM. The simulations show the
morphology and structure of the different ISM phases and reproduce many of the
features that have been observed in the Milky Way and other galaxies. In
particular, they show that the hot gas has a moderately low volume filling
factor (~20%) even in the absence of magnetic fields. Also, cold gas is mainly
concentrated in filamentary structures running perpendicular to the midplane
forming and dissipating within 10-12 Myr. Compression is the dominant process
for their formation, but thermal instability also plays a role. Also the
evolution of the Local Bubble is simulated by multi-supernova explosions;
calculated extensions after ~13 Myr match observations.
