There is the hope that Molecular electronics would enable the fabrication of ultra-small sized functional molecular circuits. However, since this is currently not easily possible using the conventional Si technology, this branch of nano-technology requires significant understanding of the various physical processes that take place on the atomic scale which are governed by quantum mechanical principles. Quantum mechanics introduces uncertainties in the behaviour and, therefore, the investigation of atomic and molecular junctions is not very straightforward. Many approaches have been developed to fabricate such junctions in a reliableway, but nevertheless, there still exists a lack of reproducibility amongst measurements. Similarly, along with the increasing miniaturisation demands, not only smaller circuits are desired, but their efficiency and performance also suffers from the increased current densities and local heating. Therefore, while investigating atomic/molecular junctions the approach within this thesis was two-fold: (a) better understanding of the mechanism of electromigration(EM) within nano-structures and (b) fabrication of reproducible atomic point contacts using EM in ultra-thin Ag structures.In this thesis, an unique set-up consisting of a 4-tip SEM/STM UHV chamber was used to perform EM measurements on nano-structures. Multiple Ag nano-structures were fabricated on a Si substrate using a two-step lithography process and presence of the in-situ SEM enabled easy navigation from one nano-structure to the other. The tips were used for contacting the structures and a feedback controlled electromigration (FCE) mechanism was used to control the voltage between them during the EM process. Significant effort was devoted on the development and integration of the EM set-up within the 4-tip SEM/STM UHV chamber inorder to establish an in-situ fabrication and characterisation technique of atomic/molecular junctions.Ag bow-tie shaped structures with a centre width between 100 - 200nm were investigated at lN2 temperatures and the in-situ characterisation of the structures was performed before and after EM. Ultra-thin Ag structures deposited on Si exhibited a granular nature with an average grain size of Ag grains between 30 - 40 nm. Therefore, the smallest constriction consisted of more than one grain, which when subjected to EM, led to a complex structure formation. It was observed from the conductance curves that even though these structures depict conductance quantisation while thinning during EM, they could not be re-used forrepeatable opening and closing of atomic junctions. This observation led to the conclusion that in order to fabricate reproducible atomic junctions, structure widths below the size of one single grain must be used. To reduce the centre widths below 30 nm, focused ion beam (FIB) patterning was employed, to reliably shape the centre constriction to widths below 20 nm. This extra nano-structuring step allowed precise in-situ local control on the morphology of the structures, which served as a step forward in defining the geometry of the atomic junctions and also improved the reproducibility of the EM technique. EM on these structures produced very well defined conductance plateaus which could be re-opened multiple times, suggesting that atomically precise metallic point contacts were generated. Hence, this dissertation addresses one of the very complex issues in molecular electronics i.e.reproducible fabrication of atomic contacts.Furthermore, CO molecule(s) were adsorbed on these point contacts. Being one of the very simple asymmetric molecules, CO served as a good candidate to understand the role of chemisorption on such junctions. Time-resolved current measurements showed bi-stabilities that were dependent on bias voltages. Conductance could be reproducibly changed between two states just by changing the operating voltage suggesting even the simplest molecular junction possesses the capability to function as switches, or memory devices. In the presentcase, the exact mechanism behind this behaviour has not been completely comprehended, but few possibilities have been outlined. Hence, this thesis also provides intriguing results on electrical properties of chemisorbed Ag atomic contacts.