Terahertz source based on parametric oscillator is an important tunable terahertz device. It has important applications in the security check, biosensors, medical diagnostics, testing and quality control of semiconductor devices. This article summarizes the experimental and theoretical research of domestic and foreign terahertz parametric oscillator in terms of the material properties of the nonlinear crystal, resonator structure, terahertz output coupler, frequency tuning mode and linewidth control. We review the cascaded terahertz parametric process in continuous, pulse, ultrashort pulse operating styles and propose some of its future research directions. With the development of fiber laser technology and periodically poled crystals to further improve the performance, the terahertz parametric oscillator will move to the direction of more efficient, small, practical, portable and easy to operate, and play an increasingly important role in its application fields.