Laser-based and electron accelerator sources provide very short and intense pulses of radiation over substantial ranges of the electromagnetic spectrum covering ten to hundreds of terahertz [Bründermann et al., “Terahertz Techniques”, Springer Series in Optical Sciences, vol. 151 (2012)]. Typically, the pulses are emitted up to high repetition rates well into the megahertz and gigahertz range leading to frequency combs [Steinmann et al., “Frequency-comb spectrum of periodic-patterned signals,” Phys. Rev. Lett. 117, 174802 (2016)]. The presentation will focus on methods for terahertz diagnostics of electron density near-fields and radiation far-fields with a special emphasis on measuring short pulses with wide terahertz frequency coverage at high repetition rates in the megahertz to gigahertz range. These continuous, high-repetition measurement methods of single-shots without interruption are readily transferable to materials research studies. Recording each single-shot avoids averaging methods and enables statistical methods used for ensembles promoting data processing techniques. Intense electric fields emitted from electron accelerator-based sources approaching GV/m also open new windows to materials research.