Optical nonlinearities are known to provide a coherent coupling between the amplitude and phase of the light, which can result in the formation of periodic waveforms. Lasers that emit such waveforms are referred to as optical frequency combs. Here we show that Bloch gain - a nonclassical phenomenon that was first predicted in the 1930s - plays an essential role in comb formation in quantum cascade lasers (QCLs). We develop a self-consistent theoretical model that considers all aspects of comb formation: bandstructure, electron transport, and cavity dynamics. It reveals that Bloch gain gives rise to a giant Kerr nonlinearity and serves as the physical origin of the linewidth enhancement factor in QCLs. Using a master equation approach, we explain how frequency modulated combs can be produced in Fabry-P��rot QCLs over the entire bias range. In ring resonators, Bloch gain triggers phase turbulence and the formation of soliton-like patterns.