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We review the development of terahertz quantum-cascade lasers (QCLs) that can be uniquely qualified based on a resonant-phonon depopulation scheme. Record performances in terms of operating temperature and optical power output are reported. The best temperature performance is achieved in the metal-metal (MM) waveguides, which provide near-unity mode confinement and low waveguiding loss at terahertz (THz) frequencies even for cavities with subwavelength dimensions. A pulsed operation up to a heat-sink temperature of 169 K at v ~ 2.7 THz and a continuous-wave (CW) operation up to 117 K at v ~ 3 THz are demonstrated with a five-level design that has a two-well injector region. Some of the key temperature degradation mechanisms for this design are discussed. For operation at lower frequencies (v < 2 THz), a one-well injector design is developed that reduces intersubband absorption losses in the injector region. A QCL operating at v = 1.59 THz (lambda = 188.5 mum) up to a heat-sink temperature of 71 K in cw mode is demonstrated with that design. To obtain high-power output and low beam divergence from the MM waveguides, a lens-coupled scheme is demonstrated. A peak power output of 145 mW, a beam width of 4.8deg, and a maximum lasing temperature of 160 K are obtained from a 4.1 THz QCL in this configuration. In the latter part of the paper, we report on the demonstration of video-rate (20 frames/s) terahertz imaging with QCLs as the source for illumination and a 320 times 240 element room-temperature microbolometer focal plane array as the detector. The QCLs for the imaging system are processed into semiinsulating surface-plasmon waveguides, and are operated in a cryogen-free thermomechanical cooler in quasi-CW mode at a heat-sink temperature of ~30 K. Real-time imaging in transmission mode is demonstrated at a standoff distance of 25 m with a v ~ 4.9 THz QCL in this setup.