In the last few decades, plasmonic nanostructures have been studied and used vividly for numerous applications ranging from medicine and diagnostics to efficiency enhancement of solar cells. In line with this, the main focus of this thesis is to investigate the applicability of plasmonic nanostructures and develop new methodologies for improving their capabilities for certain specific physical and biological applications. Biosensing is one of the areas which has benefited significantly from the plasmonic resonances supported by those nanostructures. Even though significant advances in sensing methods have been made, the detection of small molecules still remains a challenging task. The first part of the thesis investigates the possibility of exploiting coupling between the resonances of plasmonic nanostructures and absorbing molecules for sensing small biologically relevant species. Both the weak and strong coupling regimes between the plasmonic resonances and the absorption bands of molecules are studied. Another principal application of plasmonic nanostructures lies in the field of medicine and diagnostics. The biocompatibility of plasmonic nanostructures is an important question that must be addressed for applications in this field. Furthermore, approaches which can improve or enhance the bio-compatibility properties of nanostructures are much sought after. It is now well known that the biocompatibility of plasmonic nanoparticles is closely associated with the coating of the molecules around the structure. A potential route for synthesis of plasmonic nanoparticles using human cells is studied in the second part of this thesis. The synthesized nanoparticles are shown to possess a rich protein coating, known as the protein corona. Preliminary experiments for understanding the uptake characteristics of the human cell synthesized nanoparticles are also performed. The next application that is investigated is the detection of nanoparticles using plasmonic nanostructures, exploiting the coupling between two plasmonic resonances. This technique allows the detection of individual 30 nm particles. The data acquired from this method could, in future, be used to complement information obtained from the traditional nanoparticle analysis techniques. On a different note, nonlinear optical processes can also be enhanced using the high near fields generated in plasmonic nanostructures. However, the conversion efficiency is strongly dependent on the modal properties of the nanostructures. For this reason, a technique for calculating the eigenmodes of a plasmonic nanoclusters is developed. The modal structure computed using the developed method is then used for analyzing and understanding second harmonic generation from the nanoparticle clusters. It is well known that the maximum obtainable enhancement of an optical process via the use of plasmonic nanostructure is limited by the amount of energy that can be trapped in its near-field. The final part of this thesis studies and exploits different ways for developing plasmonic nanostructures which absorb all the incident energy at a given wavelength. When a nanostructure is illuminated with two incident beams simultaneously, it is possible to exploit the phenomenon of destructive interference to achieve perfect absorption. This is demonstrated both theoretically and experimentally. [...]