Abstract: This paper presents an overview of recent results for NbN phonon-cooled hot electron bolometric (HEB) mixers. The noise temperature of the receivers based on both quasioptical and waveguide versions of HEB mixers has crossed the level of 1 K GHz−1 at 430 GHz (410 K), 600–650 GHz (480 K), 750 GHz (600 K), 810 GHz (780 K) and is close to that level at 1.1 THz (1250 K) and 2.5 THz (4500 K). The gain bandwidth measured for quasioptical HEB mixer at 620 GHz reached 4 GHz and the noise temperature bandwidth was almost 8 GHz. Local oscillator power requirements are about 1 μW for mixers made by photolithography and about 100 nW for mixers made by e-beam lithography. A waveguide version of 800 GHz receiver was installed at the Submillimeter Telescope Observatory on Mt. Graham, AZ, to conduct astronomical observations of known submillimeter lines (CO, J=7→6, CI, J=2→1). It was proved that the receiver works as a practical instrument.