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The push to continually improve computing power through the further miniaturisation of electronic devices has led to an explosion of "post-Moore" technologies such as molecular electronics and quantum computing. The downscaling of electronic devices has enhanced the importance of quantum effects. As a result to aid in the understanding and development of new devices, accurate and efficient atomistic material modelling methods are crucial for guiding experiments. In this thesis first principle material modelling (e.g Density Functional Theory) is combined with the atomistic Non Equilibrium Green's Function quantum transport method to study how the electronic structure of two interesting junction systems relate to the electron transport through the junction. These two types of junctions, molecular and metal oxide, have crucial roles to play in the development of molecular based memories and superconducting quantum computing respectively. The first half of this thesis shows how the electronic structure of Polyoxometalate molecules dominate their electron transport properties whilst their redox ability makes them promising for memory applications. The results of the simulations reveal how the charge-balancing counterions of Polyoxometalates increase the conductance of the molecular junctions by stabilisation of unoccupied states, this is a key discovery as the effect of counterions are typically ignored. Polyoxometalates can be altered easily by changing the identity of the central caged atom, enhancing device engineering possibilities. The IV characteristics and capacitance are computed for Polyoxometalates with different caged atoms, the results show how the charge transport and storage can be engineered by choice of caged species and redox state. In the second half of this work, the archetypal Josephson junction, Al/AlOx/Al is explored. The goal was to understand from an atomistic point of view how the nature of the amorphous barrier influences the electron transport. The calculations provide evidence that the oxide concentration of the amorphous barrier significantly influences the resistance of the junction, it is found that oxygen deficient barriers lead to higher than expected critical currents. Unexpectedly the simulations here fail to show an exponential relationship between barrier length and resistance of the device. It is argued that there is an effective barrier length smaller than the physical barrier length due to thinner regions of the barrier. This highlights how important an understanding of the atomic structure of these junctions are for designing high quality junctions for superconducting qubits.