Abstract: We review the latest developments, research, and radioastronomy applications of hot-electron bolometer (HEB) mixers operated in the terahertz waveband. The physical principles of operation of terahertz HEB mixers are presented, their manufacturing from ultrathin NbN films, the main HEB-mixer parameters and their measurement techniques are discussed, and practical terahertz radioastronomy projects based on heterodyne receivers with HEB mixers are considered.