  Strong evidence for cooling flows has been found in low resolution X-ray
imaging and spectra of many clusters of galaxies. However high resolution X-ray
spectra of several clusters from the Reflection Grating Spectrometer (RGS) on
XMM-Newton now show a soft X-ray spectrum inconsistent with a simple cooling
flow. The main problem is a lack of the emission lines expected from gas
cooling below 1--2 keV. Lines from gas at about 2--3 keV are observed, even in
a high temperature cluster such as A 1835, indicating that gas is cooling down
to about 2--3 keV, but is not found at lower temperatures. Here we discuss
several solutions to the problem; heating, mixing, differential absorption and
inhomogeneous metallicity. Continuous or sporadic heating creates further
problems, including the targetting of the heat at the cooler gas and also the
high total energy required. So far there is no clear observational evidence for
widespread heating, or shocks, in cluster cores, except in radio lobes which
occupy only part of the volume. The implied ages of cooling flows are short, at
about 1 Gyr. Mixing. or absorption, of the cooling gas are other possibilities.
Alternatively, if the metals in the intracluster medium are not uniformly
spread but are clumped, then little line emission is expected from the gas
cooling below 1 keV. The low metallicity part cools without line emission
whereas the strengths of the soft X-ray lines from the metal-rich gas depend on
the mass fraction of that gas and not on the abundance, since soft X-ray line
emission dominates the cooling function below 2 keV.
