The structural, vibrational, and electronic properties of anisotropic materials under compression are comprehensively investigated in this thesis. Recent developments in the techniques of high-pressure X-ray diffraction and Raman scattering, and significant advances in first principle simulations provide detailed high-pressure studies of condensed matter systems. In view of the widely disparate strength of cohesive forces, these studies consist of ionic compounds, quasi-two dimensional semiconductors, quasi-molecular solids, and end with liquid crystals. As a result of the coexistence of different hierarchical interactions in anisotropic systems, evidence of preferential pressure-induced enhancement of weak bonding is found not only in the structural response to external hydrostatic pressure but also in vibrational and electronic behaviour. Further, the understanding of pressure-induced breakdown of rigid-layer vibrations (explored in layered compounds), pressure-induced electron transfer in molecular crystals, and strong overlap of inter- and intra-molecular vibrational modes of liquid crystals provides insight into the essential physics of flexible molecular systems.