Exploration of the far-infrared region of the electromagnetic spectrum has been frustrated by the difficulty of generating and detecting radiation at terahertz frequencies (0.1 to 10 THz). Researchers had to contend with low-brightness thermal sources or narrow-bandwidth molecular lasers to produce radiant energy in this region, and with low-sensitivity cryogenic bolometers for detection. Conditions began to change in the early 1990s with the advent of ultrafast optoelectronic techniques for producing and detecting terahertz radiation, or T-rays. One promising method, terahertz time-domain spectroscopy, uses femtosecond pulses of laser light to generate and detect single-cycle bursts of terahertz radiation with a pair of photoconductive transducers. This approach, pioneered at AT&T Bell Labs in Holmdel, N.J., and IBM's Thomas J. Watson Research Center in Yorktown Heights, N.Y., can create a spatially coherent, broadband beam of terahertz frequencies from approximately 0.1 to more than 5 THz. Furthermore, it can detect the radiation with a signal-to-noise ratio of 10,000:1 without cryogenic cooling or shielding. The technique's broad bandwidth, spatial coherence and exceptional sensitivity are useful in spectroscopic studies of many physical systems and materials, including some that have never before been characterized in this spectral range. For example, the gated coherent detection scheme permits far-infrared spectroscopy of hot objects such as flames and plasmas, the incoherent radiation from which would ordinarily swamp conventional detectors. But perhaps the most exciting application is in imaging objects by scanning them with T-rays, which can be focused, collimated, transmitted and reflected just like laser beams. Terahertz imaging opens a window of exploration for science, biomedicine, industry, electronics and quality control. The development of a commercial T-ray system with almost two decades of usable bandwidth from 0.03 to 2 THz should help motivate the development of many more applications that exploit the power and versatility of terahertz time-domain spectroscopy.