Terahertz parametric source is a laser driven terahertz wave radiation source, which has many advantages such as high coherence, wide tunability and room temperature operation, etc. After a brief introduction to basic principle of terahertz parametric sources, this paper mainly summarizes the recent representative research results about terahertz parametric sources, including: 1) Commonly used nonlinear crystals including lithium niobate, potassium titanium phosphate, potassium titanyl arsenate, rubidium titanium phosphate; 2) Large pulse energy terahertz parametric sources. The main generation methods include using surface-emitted structure, using ring cavity, increasing the damage threshold of the nonlinear crystal, etc. The largest reported terahertz energy reaches 17 μJ; 3) High average power terahertz parametric sources. The main generation methods include deploying laser diode side-pumped laser as the pumping source, balancing the increase of the pulse energy and pulse repetition rate simultaneously, etc. The highest terahertz average power reported reaches 367 μJ till now; 4) Theoretical simulation on different kinds of terahertz source structures. Mainly based on the coupled wave equations, thetheoretical models for terahertz parametric generator, injection-seeded parametric generator, intracavity-pumped and extracavity-pumped terahertz parametric oscillators are introduced respectively.