  We discuss new results from the Chandra X-ray Observatory and XMM-Newton on
cluster cooling flows, emphasizing early results from our Chandra programs. We
find cooling rates reduced by factors of 5-10 compared to those from earlier
missions. Nevertheless, substantial amounts of keV gas appear to be cooling and
fueling star formation in central dominant cluster galaxies (CDGs). The
structure of the keV thermal gas is remarkably complex, particularly in regions
surrounding the the radio source and sites of star formation in CDGs. The radio
sources are displacing the thermal gas leaving cavities filled with radio
emission. The cavities are apparently supported against the local gas pressure
by magnetic fields and cosmic rays. In addition, radio-faint, ``ghost''
cavities are seen in some clusters. They may be relics of earlier radio
outbursts rising buoyantly in the intracluster medium. The radio sources may
reduce the mass deposition rates by mechanical heating, and by inducing
convective currents that move cool material outward.
