The High Energy cosmic-Radiation Detection (HERD) is a future space experiment which will be installed on the China’s Space Station around 2027. The main goal of the experiment is the measurement of cosmic rays up to energies which are not explored by the instruments currently operating in space, in particular protons with energies up to PeV, nuclei up to hundreds of TeV per nucleon and electrons up to tens of TeV. HERD will consist of silicon charge detectors, anti-coincidence scintillators, scintillating fiber trackers, a transition radiation detector and a calorimeter. The latter is a homogeneous, deep, 3D segmented calorimeter made of about 7500 LYSO cubic crystals: thanks to this innovative design, it will achieve large acceptance, good energy resolution and excellent electron/proton discrimination. In order to increase both energy calibration capabilities and redundancy of the instrument, the LYSO scintillation light will be read-out by two independent systems: the first is made of wave-length shifting fibers coupled with imaged intensified CMOS cameras, and the second one consists of photodiodes with different active areas connected to a custom front-end electronics. Both read-out systems are designed to have a large dynamic range, up to $10^7$, and a low power consumption. The design of the calorimeter is validated by several Monte Carlo simulations and beam test results obtained with detector prototypes. In this paper we describe the anticipated performances of the calorimeter and the current status of the double read-out system, and we discuss the recent developments of both the HERD prototype and the flight model design.