Graphene is foreseen to be the basis of future electronics owing to its ultra thin structure, extremely high charge carrier mobility,  high thermal conductivity etc., which are expected to overcome the size limitation and heat dissipation problem in silicon based transistors. But these great prospects are hindered by the metallic nature of pristine graphene even at charge neutrality point, which allows to flow current even when a transistor is switched off. A part  of the thesis is dedicated to invoke electronic band gaps in graphene to overcome this problem. The concept of quantum confinement has been employed to tune the band gaps in graphene by  dimensional confinement along with the functionalization of the edges of these confined nanostructures. Thermodynamic stability of the functionalized zigzag edges with hydrogen, fluorine and reconstructed edges has been presented in the thesis. Keeping an eye towards the same goal of band gap opening,  a different route has been considered by admixing insulating hexagonal boron nitride (h-BN) with semimetal graphene. The idea has been implemented in two  dimensional h-BN-graphene composites and three dimensional stacked heterostructures. The study reveals the possibility of tuning band gaps by controlling the admixture. Occurrence of defects in graphene has significant effect on its electronic properties. By random insertion of defects, amorphous graphene is studied, revealing a semi-metal to a metal transition. The field of molecular electronics and spintronics aims towards device realization at the molecular scale. In this thesis, different aspects of magnetic bistability in organometallic molecules have been explored in order to design  practical spintronics devices. Manipulation of spin states in organometallic molecules, specifically metal porphyrin molecules, is achieved by controlling surface–molecule interaction. It has been shown that by strain engineering in defected graphene, the magnetic state of adsorbed molecules can be changed. The spin crossover between different spin states can also be achieved by chemisorption on magnetic surfaces. A significant part of the thesis demonstrates that the surface-molecule interaction not only changes the spin state of the molecule, but allows to manipulate magnetic anisotropies and spin dipole moments via modified ligand fields. Finally, in collaboration with experimentalists, a practical realization of switching surface–molecule magnetic interactions by external magnetic fields is demonstrated.