In this contribution we trace the evolution of cool-core clusters out to z~1.3 using high-resolution Chandra data of three representative cluster samples spanning different redshift ranges. Our analysis is based on the measurement of the surface brightness (SB) concentration, c_SB, which strongly anti-correlates with the central cooling time and allows us to characterize the cool-core strength in low S/N data. We confirm a negative evolution in the fraction of cool-core clusters with redshift, in particular for very strong cool-cores. Still, we find evidence for a large population of well formed cool-cores at z ~ 1. This analysis is potentially very effective in constraining the nature and the evolution of the cool-cores, once large samples of high-z clusters will be available. In this respect, we explore the potential of the proposed mission Wide Field X-ray Telescope (WFXT) to address this science case. We conclude that WFXT provides the best trade-off of angular resolution, sensitivity and covered solid angle in order to discover and fully characterize the cool-core cluster population up to z=1.5.
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