Recent results in the field of three-frequency wave interaction in homogeneous and inhomogeneous (periodically poled) active nonlinear crystals with quadratic nonlinearity are reviewed. The quasi-phase-matched processes of self-frequency doubling, self-frequency halving, and frequency mixing of the pump and laser radiations are studied. The consecutive quasi-phase-matched processes of the third-harmonic generation and parametric amplification with low-frequency pumping in periodically poled active nonlinear crystals are also investigated. The analysis is carried out for the case of a periodically poled Nd:Mg:LiNbO3 crystal. Perspectives of using periodically poled active nonlinear crystals in laser devices with self-frequency conversion are discussed.