The analysis of nature of bonding in non-classical structures is always an intriguing area of research. Typical examples of such systems are polyhedral boranes that exhibit fascinating cluster bonding where the traditional 2-center-2-electron (2c-2e) bond model fails. This thesis involves the investigation of such polyhedral borane structures and their reactivity by employing both qualitative and quantitative tools of electronic structure theory. There is an intense current interest in the macropolyhedral boranes for their applications pharmaceuticals and materials chemistry. The mno rule had been formulated to account for the electronic requirements for the macropolyhedral structures. Though useful in explaining and designing structures, electron counting rules provide a yes or no answer; not all the molelcules having stipulated number of electrons are equally stable. We have used the concept of orbital compatibility to explain the relative energies of different macropolyhedral structural patterns such as closo-closo, closo-nido and nido-nido. One of the major problems in polyhedral boron cage chemistry has been the lack of general synthetic routes for the construction of large cage systems . With this view, we explored the mechanism of the reaction of macropolyhedron B20H16 with MeCN and similar ligands, which provide an understanding of the skeletal rearrangement that occur in macropolyhedral boranes. This can help in the design and synthesis of new macropolyhedral boranes. The early examples of metallaboranes were found to adopt structures which are analogous to that of boranes and carboranes. Hypercloso metallaboranes have closo structure with less number of electrons than required by Wades rule. We have carried out a detailed DFT analysis to explore the structure and electronic relationship of 9-12 vertex closo and hypercloso structures of both borane and metallaboranes. Calculations show that in vertex hypercloso metallaborane needs only n skeleton electron pairs rather than n+1 as suggested by Wade’s rules. Stabilization of supraicosahedral boranes with more than 12 vertices by substituting BH groups by transition metal fragments is also explored with DFT calculations. Calculations show that as the number and the size of the metal atom increases the stability of supraicosahedral and condensed supraicosahedral borane structures also increases. These studies will open up new possibilities for the development of polyhedral clusters of extraordinary size.