With centre-of-mass energies covering the Z pole, the WW threshold, the HZ production, and the top-pair threshold, the FCC-ee offers unprecedented possibilities to measure the properties of the four heaviest particles of the Standard Model (the Higgs, Z, and W bosons, and the top quark), and also those of the b and c quarks and of the $tau$ lepton. At these moderate energies, the role of the calorimeters is to complement the tracking systems in an optimal (a.k.a. particle-flow) event reconstruction. In this context, precision measurements and searches for new particles can fully profit from the improved electromagnetic and hadronic object reconstruction offered by new technologies, finer transverse and longitudinal segmentation, timing capabilities, multi-signal readout, modern computing techniques and algorithms. The corresponding requirements arise in particular from the resolution on reconstructed hadronic masses, energies, and momenta, e.g., of H, W, Z, needed to reach the FCC-ee promised precision. Extreme electromagnetic energy resolutions are also instrumental for $pi^0$ identification, $tau$ exclusive decay reconstruction, and physics sensitivity to processes accessible via radiative return. We present state of the art, challenges and future developments on some of the currently most promising technologies: high-granularity silicon and scintillator readout, dual readout, noble-liquid and crystal calorimeters.
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