The development of teranertz (THz) quantum cascade lasers (QCLs) has progressed considerably since their advent almost a decade ago. THz QCLs operating in a frequency range from 1.4 to 4 THz with electron-phonon scattering mediated depopulation schemes are described. Several different types of GaAs/AlGaAs superlattice designs are reviewed. Some of the best temperature performances are obtained by the so-called resonant-phonon designs that are described. Operation above a temperature of 160 K has been obtained across the spectrum for THz QCLs operating at \nu >1.8 THz. The maximum operating temperature of previously reported THz QCLs has empirically been limited to a value of ~\hbar \omega/kB. A new design scheme for THz QCLs with scattering-assisted injection is shown to surpass this empirical temperature barrier, and is promising to improve the maximum operating temperatures of THz QCLs even further.