Over the past three decades a new spectroscopic technique with unique possibilities has emerged. Based on coherent and time-resolved detection of the electric field of ultrashort radiation bursts in the far-infrared, this technique has become known as terahertz time-domain spectroscopy (THz-TDS). In this review article the authors describe the technique in its various implementations for static and time-resolved spectroscopy, and illustrate the performance of the technique with recent examples from solid-state physics and physical chemistry as well as aqueous chemistry. Examples from other fields of research, where THz spectroscopic techniques have proven to be useful research tools, and the potential for industrial applications of THz spectroscopic and imaging techniques are discussed.