Two lines of evidence indicate that active galaxies, principally radio galaxies, have heated the diffuse hot gas in clusters. The first is the general need for additional heating to explain the steepness of the X–ray luminosity–temperature relation in clusters, the second is to solve the cooling–flow problem in cluster cores. The inner core of many clusters is radiating energy as X–rays on a time–scale much shorter than its likely age. Although the temperature in this region drops by a factor of about three from that of the surrounding gas, little evidence is found for gas much cooler than that. Some form of heating appears to be taking place, probably by energy transported outward from the central accreting black hole or radio source. How that energy heats the gas depends on poorly understood transport properties (conductivity and viscosity) of the intracluster medium. Viscous heating is discussed as a possibility. Such heating processes have consequences for the truncation of the luminosity function of massive galaxies.