  The Advanced Telescope for High-Energy Astrophysics (Athena) has been
selected by ESA as its second large-class mission. The future European X-ray
observatory will study the hot and energetic Universe with its launch foreseen
in 2028. Microcalorimeters based on superconducting Transition-edge sensor
(TES) are the chosen technology for the detectors array of the X-ray Integral
Field Unit (X-IFU) on board of Athena. The X-IFU is a 2-D imaging
integral-field spectrometer operating in the soft X-ray band (0.3 -12 keV). The
detector consists of an array of 3840 TESs coupled to X-ray absorbers and read
out in the MHz bandwidth using Frequency Domain Multiplexing (FDM) based on
Superconducting QUantum Interference Devices (SQUIDs). The proposed design
calls for devices with a high filling-factor, high quantum efficiency,
relatively high count-rate capability and an energy resolution of 2.5 eV at 5.9
keV. The paper will review the basic principle and the physics of the TES-based
microcalorimeters and present the state-of-the art of the FDM read-out.
