From the beginning of the study of X-ray emission from clusters of galaxies, Andy Fabian has made a very large number of crucial contributions. This is particularly true of the study of cool cores in clusters. In this review, the X-ray properties of clusters will be briefly summarized. I will then discuss some recent observations, current areas of interest, and outstanding scientific problems. Recent observations of the central regions of cool cores and of the interaction between the radio sources and X-ray gas will described. The presence of cooler gas and newly formed stars, and the relation to the X-ray emitting gas will be discussed. Mechanisms for the feedback of energy from central AGNs and for heating the gas will be considered. On larger scales, recent results on the effects of mergers on clusters will be reviewed. I will discuss the possible detections of nonthermal emission in both the hard and soft X-ray bands, and present some new results.