In this thesis both computational (Density Functional Theory calculations on isolated systems and on crystals) and experimental (Infrared and Raman spectroscopy and Differential Thermal Analysis) methods were used to analyse insulating crystalline solids, with particular focus on their structural and vibrational properties. In the first part, the effects of physical and chemical pressure on the structure and the vibrational spectra of the Matlockite-type compounds MFX (M=Ba, Sr and X=Cl, Br) were studied using periodic-DFT calculations. Further studies concerned BaxFyClz compounds and the phase diagram BaCl2-BaF2. In the second part of this thesis A2TH6 systems, (A= alkaline earth and T=Fe, Ru) and borohydrides were considered. In particular, many borohydrides were studied both experimentally and theoretically. New insights on spectra-structure relations were obtained.