  The ISM, powered by SNe, is turbulent and permeated by a magnetic field (with
a mean and a turbulent component). It constitutes a frothy medium that is
mostly out of equilibrium and is ram pressure dominated on most of the
temperature ranges, except for T< 200 K and T> 1E6 K, where magnetic and
thermal pressures dominate, respectively. Such lack of equilibrium is also
imposed by the feedback of the radiative processes into the ISM flow. Many
models of the ISM or isolated phenomena, such as bubbles, superbubbles, clouds
evolution, etc., take for granted that the flow is in the so-called collisional
ionization equilibrium (CIE). However, recombination time scales of most of the
ions below 1E6 K are longer than the cooling time scale. This implies that the
recombination lags behind and the plasma is overionized while it cools. As a
consequence cooling deviates from CIE. This has severe implications on the
evolution of the ISM flow and its ionization structure. Here, besides reviewing
several models of the ISM, including bubbles and superbubbles, the validity of
the CIE approximation is discussed, and a presentation of recent developments
in modeling the ISM by taking into account the time-dependent ionization
structure of the flow in a full-blown numerical 3D high resolution simulation
is presented.
