Crystalline materials are known for their well-defined periodic structure and their properties have been widely applied in numerous fields. An ideal single crystal will exhibit a perfect ordered structure. However, in most crystalline materials defects and dislocations are commonly present and the vast majority of applications of crystalline materials concern polycrystalline materials rather than single crystals. In metals the effects of disorder and polycrystallinity have been studied extensively, but the effect on the properties of other crystals, such as organic molecular materials, are not fully understood. In this thesis the techniques of low-frequency vibrational spectroscopy by means of terahertz time-domain spectroscopy (THz-TDS) were combined with density functional theory (DFT) simulations to investigate the role and effect of disorder for small organic molecular materials including drug molecules as well as other emerging materials. Terahertz radiation is located between the far-infrared and microwave regions on the electromagnetic spectrum. At these frequencies photons excite a complex mix of inter- and intra-molecular interactions in solid state materials, particularly low-frequency vibrational modes in molecular crystals. Due to the complexities of lattice vibrations at such low frequencies, high-accuracy computational methods are necessary to interpret the experimental results. Such simulations are usually based on ideal, defect free, structures of crystals while experiments are performed on commercial or lab-synthesised samples that will exhibit some disorder. Careful comparison between the results from the ideal calculations and the experimental observation makes it possible to study the role of defects in the crystalline systems of interest. In this context THz-TDS can be considered as a complementary method to the classical crystallographic techniques, e.g. X-ray diffraction, to aid the effective structural analysis of crystals. The methodologies that were developed in this thesis are useful to provide more information for the design and the performance of novel materials such as metal-organic frameworks (MOFs) in general and MOF perovskites in particular from the perspective of low-frequency vibrations. This is meaningful for the future optimisation and screening of materials. For small organic molecules, the new method is helpful to better understand the mechanism of their phase transitions and to determine the structure of polymorphs, even in the presence of disorder. This idea is explored to investigate the fundamentals of the crystallisation process where the sensitivity of terahertz spectroscopy to both crystalline structure as well as liquid dynamics is exploited to gain further insight into the transition between disorder and order.