Beginning from the 1990s, an ever-lasting interest in the THz spectroscopy and THz instruments has produced wide progress in the development of high-speed THz detectors. The constantly growing requirements aimed at the increase of spectral resolution, sensitivity, and acquisition rate of THz detectors have attracted much attention in this field till nowadays. In the present review, we summarize the most recent advances in the THz photodetectors based on semiconductor structures with quantum confinement of an electron gas. Their main advantages over existing detectors are fast response time, increased spectral resolution, and multicolor operation thanks to the variability of their designs and band structure engineering. These all allow using them in various important applications as single photon detection, THz heterodyne detection, continuous monitoring of toxic gases, THz free space communications, and radio astronomy, as well.