Recent events have accelerated the quest for ever more effective security screening to detect an increasing variety of threats. Many techniques employing different parts of the electromagnetic spectrum from radio up to X- and gammaray are in use. Terahertz radiation, which lies between microwave and infrared, is the last part to be exploited for want, until recently, of suitable sources and detectors. This paper describes practical techniques for Terahertz imaging and spectroscopy which are now being applied to a variety of applications. We describe a number of proof-of-principle experiments which show that Terahertz imaging has the ability to use very low levels of this non-ionising radiation to detect hidden objects in clothing and common packing materials and envelopes. Moreover, certain hidden substances such as plastic explosives and other chemical and biological agents may be detected from their characteristic Terahertz spectra. The results of these experiments, coupled with availability of practical Terahertz systems which operate outside the laboratory environment, demonstrate the potential for Terahertz technology in security screening and counterterrorism.