%0 Journal Article %J Laser & Photonics Reviews %D 2021 %T Laser Frequency Combs with Fast Gain Recovery: Physics and Applications %A Piccardo, Marco %A Federico Capasso %K frequency-modulated combs %K harmonic state %K Quantum cascade lasers %K semiconductor laser frequency combs %K semiconductor ring lasers %K Solitons %X  The dynamics of semiconductor lasers with fast gain is generally considered to suppress amplitude modulation, resulting in a frequency-modulated output. Since their first demonstration of frequency comb operation, quantum cascade lasers—ideal representatives of this class of lasers with fast gain dynamics—were indeed shown to emit frequency-modulated combs. The understanding of these frequency comb regimes has progressively evolved, being refined from simpler arguments to more advanced theories, considering the role of Kerr nonlinearity and linewidth enhancement factor. By now, the traditional frequency-modulated combs are rather well understood in quantum cascade lasers, but new types of frequency combs have emerged, reopening interesting physics questions in these lasers. Recent advancements on two open frontiers will be discussed: harmonic frequency combs, characterized by mode skipping of many free spectral ranges, and spatiotemporal structures with solitonic features, recently reported in unidirectional ring cavities. These new types of frequency combs open technological and fundamental perspectives, sprouting new interest in quantum cascade lasers. %B Laser & Photonics Reviews %P 2100403 %G eng %U https://onlinelibrary.wiley.com/doi/abs/10.1002/lpor.202100403 %R https://doi.org/10.1002/lpor.202100403