We discuss various intracavity optical nonlinearities up to the third order in quantum-cascade lasers. The discussions are based on two kinds of nonlinearities, each toward respective applications. The susceptibilities at the second-harmonic or third-harmonic frequencies lead to harmonic generation for multicolor emission; moreover, the third-order susceptibility at the fundamental frequency results in a nonlinear refractive index, i.e., the Kerr nonlinearity, which is associated with self-pulsations in quantum-cascade lasers. The review surveys the technology progression for the enhancement of nonlinear frequency generation as well as the investigation of the physics behind the multimode output of quantum-cascade lasers. In addition, a simulation model accounting for intracavity nonlinear interactions in quantum-cascade lasers is introduced, which can be used to evaluate and further optimize the nonlinear performance.