The terahertz regime, as a last radio window, remains to be fully explored, and astronomical and atmospheric observations in this regime are scientifically important. Like other frequency regimes, developing high-sensitivity detectors (coherent and incoherent) is of particular significance for both ground-based and space-borne facilities. As the coherent detector of choice below 1.4 THz, superconductor-insulator-superconductor (SIS) heterodyne mixers have achieved as high a sensitivity as five times the quantum limit around 1.4 THz. It is, however, still a challenge to developing SIS mixers at frequencies beyond 1.4 THz with considerable transmission loss in superconducting circuits due to the Cooper-pair breaking by energetic photons and increased many difficulties in designing and fabricating. So far, superconducting hot electron bolometer (HEB) mixers have been the most sensitive heterodyne detectors at frequencies above 1.5 THz, and successfully used to detect molecular spectral lines up to 2.5 THz from ground-based and space telescopes. Although spiral-antenna coupled NbN HEB mixers show a good sensitivity in the whole THz frequency range, the directly measured spectral response with Fourier transform spectrometer falls quickly as frequency increases, especially above 3 THz. The terahertz band is also of particular importance to observe astronomical objects such as cosmic microwave background, early distant objects, cold objects and dusty objects. Aiming at such objects, we develop a terahertz imaging array system by combining advanced superconducting detectors such as transition edge sensor (TES) and microwave kinetic inductance detectors (MKIDs), thus the system has a frequency band centred at 350 m, an operational temperature of 0.3 K, and a sensitivity reaching background limit performance for ground-based applications. In addition, it is expected to have some breakthroughs in ultra-sensitive superconducting TES and MKID, low noise multi-channel readout and multiplexing, efficient terahertz-wave coupling technology, and large-scale array system integration. The developed terahertz imaging array system will serve as the next-generation instrument of Dome A 5 m terahertz telescope, conducting a 350 m-band legacy survey for studying the planets, stars, galaxies and cosmology. Besides the application in astronomy, the developed terahertz imaging array system can also be applied to some areas requiring rapid detection such as security, deep space exploration, and biomedical imaging. In this paper, we mainly introduce the superconducting detectors developed at Purple Mountain Observatory and those for international collaborative projects.