Solid oxide fuel cells are of technological interest as they offer high efficiency for energy conversion in a clean way. Understanding fundamental aspects of oxygen self-diffusion in solid state ionic systems is important for the discovery of next-generation electrolyte and cathode material compositions and microstructures that can enable the operation of SOFCs at lower temperatures more efficiently, durably, and economically. In the present perspective article, we illustrate the important role of modelling and simulations in providing direct atomic scale insights on the oxygen ion transport mechanisms and conduction properties in the cathode and electrolyte materials, and in accelerating the progress from old materials to new concepts. We first summarize the ionic transport mechanisms in the traditional cathode and electrolyte materials which have been widely studied. We then pay our attention to the non-traditional materials and their oxygen transport paths from recent studies, focusing on structural and transport anisotropy and lattice dynamics. Lastly, we highlight the new developments in the potential to increase the ionic conductivity of the traditional materials through external mechanical stimuli, bringing about the mechano-chemical coupling to drive fast ionic transport.