Star Formation in Cluster Cooling Flows

New X-ray observations from the Chandra and XMM-Newton observatories have shown that cooling of the intracluster medium is occurring at rates that are now approaching the star formation rates measured in cD galaxies at the bases of cooling ows. Star formation proceeds in repeated episodes, possibly indicating an intermit-tent fuel supply. Coupled with new evidence for heating by AGN, a new paradigm of self-regulated cooling and star formation in cluster cores is emerging. 1. The Cooling Flow Problem Little has changed in our understanding of star forma-tion in cooling ows since the topic was last reviewed at the meeting on cooling ows at Haifa in 1996. How-ever, the nature of the so-called \cooling ow problem" has changed dramatically since then. This controver-sial problem concerns the decit between the large cool-ing rates of the keV gas in the centers of clusters and the much smaller star formation rates observed in cen