This paper briefly examines methods for the generation of pulsed terahertz radiation and principles of pulsed terahertz spectroscopy, an advanced informative method for studies of complex biological and nanostructured systems. Some of its practical applications are described. Using a number of steroid hormones as examples, we demonstrate that terahertz spectroscopy in combination with molecular dynamics methods and computer simulation allows one to gain information about the structure of molecules in crystals. A 'terahertz colour vision' method is proposed for analysis of pulsed terahertz signals reflected from biological tissues and it is shown that this method can be effectively used to analyse the properties of biological tissues and for early skin cancer diagnosis.