Dielectric properties are fundamental to understanding the interaction between electric fields and materials. Infrared (IR) spectroscopy has long been employed to investigate the structure and dynamics of crystals and molecules and is often combined with Raman and terahertz (THz) spectroscopy to provide a comprehensive picture. In industrial applications, dielectric materials are pivotal across various domains, including pigments, capacitors, optical coatings, and optical fibers. More recently, the development of low-dielectric materials has gained attention, particularly for high-speed communication technologies. In this chapter, we introduce the basic concepts of dielectric properties and explore the history of their theoretical calculation. The physical origins of the dielectric response are electronic, atomic, and orientational polarizations. In this thesis, we concentrate on the atomic polarization, where the interplay of atoms and electrons is important. We also provide an overview of two key methods for calculating dielectric properties from first-principles: the anharmonic phonon method and the molecular dynamics method. Lastly, we describe the purpose of this thesis.