Attenuated total reflection infrared (ATR-IR, 4000–400 cm–1), ATR-far-IR (ATR-FIR, 400–50 cm–1), and Raman spectra (4000–10 cm–1) were measured for calcium carbonate, three kinds of minerals (calcite, aragonite, and quartz), two kinds of rocks (obsidian and pumice), and four kinds of biogenic minerals, i.e., coral (aragonite), Ruditapes philippinarum (aragonite), Meretrix lusoria (aragonite), and Corbicula japonica (aragonite), to investigate the polymorphism of minerals and biogenic minerals, differences in the crystal structure among aragonite and aragonite biogenic minerals, water in the minerals and biogenic minerals, Boson peaks of obsidian and pumice, very small amounts of carotenoids in the three kinds of shells, and so on. In this study, we put some emphasis on the low-frequency region of IR (FIR) and Raman spectra. ATR-FIR spectra were measured down to 50 cm–1 and Raman spectra were obtained down to 10 cm–1. Second derivative spectra were calculated for the FIR spectra. It has been found from the present study that the FIR spectra are the most powerful for exploring polymorphism and differences in the crystal structure among aragonite and aragonite biogenic minerals. A Boson peak, which is a characteristic low-frequency Raman band for amorphous materials, was observed at around 40 cm–1 in the Raman spectra of obsidian and pumice. The Boson peak of pumice is located at a lower frequency by 12 cm–1 than that of obsidian, indicating that the mean atomic volume of pumice is larger than that of obsidian. The present study has revealed that IR spectra are useful to investigate the amounts and structure of fluid and bound water. Moreover, it has also been found that Raman spectra can detect a very tiny amount of carotenoids in the shells due to the resonance Raman effect.