Clusters constitute an intermediate state of matter between molecules and solids whose properties are size dependent and can be tailored. In recent years, cluster science has become one of the most exciting areas of research since their study can not only bridge our understanding between atoms and their bulk but also between various disciplines. In addition, clusters can serve as a source of new materials with uncommon properties. This dissertation deals with an in-depth study of clusters as a bridge across physics, chemistry, and materials science and provides a fundamental understanding of the structure-property relationships by focusing on three different topics. The first topic deals with superatoms which are clusters that mimic the chemistry of atoms. I show that superhalogens and superalkalis can be designed to mimic the chemistry of halogen and alkali atoms, respectively. An entirely new class of salts can then be synthesized by using these superatoms as the building blocks. I have also explored the possibility of designing highly electronegative species called hyperhalogens by using superhalogens as ligands or superalkalis as core and a combination of both. Another aspect of my work on superatom is to examine if traditional catalysts (namely Pd) can be replaced by clusters composed of earthabundant elements (namely Zr and O). This is accomplished by comparing the electronic structure and reactivity of Pd clusters with isoelectronic ZrO clusters. The second topic deals with a study of the electronic structure of coinage metal (Cu and Ag) clusters and see if they remain unchanged when a metal atom is replaced by an isoelectronic hydrogen atom as is the case with Au-H clusters. The third topic deals with clusters as model of polymeric materials to understand their gas storage and sequestration properties. This is accomplished by studying the trapping of H2, CO2, CH4 and SO2 molecules in borazine-linked polymers (BLPs) and benzimidazole-linked polymers (BILPs). The first two topics provide a bridge between physics and chemistry, while the third topic provides a bridge to materials science.