We introduce several types of terahertz- (THz) wave parametric sources. THz-waves can be generated by optical parametric processes based on laser light scattering from the polariton mode of nonlinear crystals. Using parametric oscillation of MgO-doped LiNbO3 crystal pumped by a nanosecond Q-switched Nd:YAG laser, we have realized broadband sources as well as coherent (narrow band) and widely tunable THz-wave sources. The THz-wave Parametric Generator (TPG) generates a broadband THz wave using a simple configuration; the THz-wave Parametric Oscillator (TPO) and the injection seeded THz-wave Parametric Generator (is-TPG) are two sources that generate coherent, widely tunable THz radiation by suitably controlling the idler wave. We report the characteristics of the oscillation and the radiation including linewidth and tunability. Further, we show the recent progress about these THz-wave parametric sources. We developed two new kinds of TPG by using compact pump sources. One TPG includes a flash-lamp-pumped multimode Nd:YAG laser with a top-hat beam profile, that allows generating high energy, broadband THz waves. Fitting in a space as small as 12 cm × 22 cm (including the pump source) this TPG outputs more than 100 pJ/pulse, which is about 100 times higher than the best results previously reported for TPG. The other has a potential to be a narrow-linewidth injection-seeded TPG, based on an laser-diode-pumped single-mode microchip Nd:YAG laser. The pump laser linewidth is below 0.009 nm and its size is 105×30×32 mm3. This allowed us to achieve a narrow-linewidth compact injection-seeded terahertz-wave parametric generator.