Several examples of terahertz (THz) spectroscopic measurement results carried out for dielectric solids are reviewed, including THz time-domain spectra of polyamide-6 composites with nm-sized clay fillers obtained by the authors. For polyamide nanocomposites, it has become clear that the dielectric loss factor shows two peaks at around 1.9 THz and 2.7 to 3.1 THz. By referring to X-ray diffraction spectra, it is assumed that the origin of the former peak is the α-phase crystal in polyamide, and that the nanofiller loading suppresses α-phase crystallization. The latter peak shifts toward a lower frequency in the nanocomposites, which indicates that the presence of strong ionic bonds between the nanofiller and the polymer matrix restrains molecular motion and increases the relaxation time. This is believed to be the main reason of superior properties of the polymer nanocomposites.