  For two decades the steady-state cooling-flow model has dominated the
literature of cluster and elliptical-galaxy X-ray sources. For ten years this
model has been in severe difficulty from a theoretical point of view, and it is
now coming under increasing pressure observationally. For two decades the
steady-state cooling-flow model has dominated the literature of cluster and
elliptical-galaxy X-ray sources. For ten years this model has been in severe
difficulty from a theoretical point of view, and it is now coming under
increasing pressure observationally. A small number of enthusiasts have argued
for a radically different interpretation of the data, but had little impact on
prevailing opinion because the unsteady heating picture that they advocate is
extremely hard to work out in detail. Here I explain why it is difficult to
extract robust observational predictions from the heating picture. Major
problems include the variability of the sources, the different ways in which a
bi-polar flow can impact on X-ray emission, the weakness of synchrotron
emission from sub-relativistic flows, and the sensitivity of synchrotron
emission to a magnetic field that is probably highly localized.
