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Quantum cascade (`QC') lasers are reviewed. These are semiconductor injection lasers based on intersubband transitions in a multiple-quantum-well (QW) heterostructure, designed by means of band-structure engineering and grown by molecular beam epitaxy. The intersubband nature of the optical transition has several key advantages. First, the emission wavelength is primarily a function of the QW thickness. This characteristic allows choosing well-understood and reliable semiconductors for the generation of light in a wavelength range unrelated to the material's energy bandgap. Second, a cascade process in which multiple - often several tens of - photons are generated per electron becomes feasible, as the electron remains inside the conduction band throughout its traversal of the active region. This cascading process is behind the intrinsic high-power capabilities of the lasers. Finally, intersubband transitions are characterized through an ultrafast carrier dynamics and the absence of the linewidth enhancement factor, with both features being expected to have significant impact on laser performance. The first experimental demonstration by Faist et al in 1994 described a QC-laser emitting at 4.3 m wavelength at cryogenic temperatures only. Since then, the lasers' performance has greatly improved, including operation spanning the mid- to far-infrared wavelength range from 3.5 to 24 m, peak power levels in the Watt range and above-room-temperature (RT) pulsed operation for wavelengths from 4.5 to 16 m. Three distinct designs of the active region, the so-called `vertical' and `diagonal' transition as well as the `superlattice' active regions, respectively, have emerged, and are used either with conventional dielectric or surface-plasmon waveguides. Fabricated as distributed feedback lasers they provide continuously tunable single-mode emission in the mid-infrared wavelength range. This feature together with the high optical peak power and RT operation makes QC-lasers a prime choice for narrow-band light sources in mid-infrared trace gas sensing applications. Finally, a manifestation of the high-speed capabilities can be seen in actively and passively mode-locked QC-lasers, where pulses as short as a few picoseconds with a repetition rate around 10 GHz have been measured.