A critical factor that influences the rate performance of batteries is the diffusion of the electroactive ions in the active materials, i.e., solid electrodes and/or electrolytes, which in turn is largely influenced by the ionic migration barriers (Em) within host frameworks. Determining Em precisely using experimental techniques, such as electrochemical impedance, variable temperature nuclear magnetic resonance, etc. is not a trivial task. Computationally, evaluating Em is often done via density functional theory (DFT)-based nudged elastic band (NEB) calculations or ab initio molecular dynamics (AIMD) simulations. Typically, DFT-NEB can yield a direct estimate of Em in a given material, while AIMD relies on statistical sampling of migration events (which becomes more difficult with increasing Em values). Hence, DFT-NEB is the preferred computational choice to determine Em. However, the accuracy of DFT-NEB calculations in estimating Em is dependent on the choice of exchange-correlation (XC) functionals, and the errors associated with using different XC frameworks has not been accurately quantified yet. Hence, in the first part of my talk, I will focus on assessing the accuracy of different XC frameworks (versus experiments) in estimating Em in a wide variety of electrode and solid electrolyte materials. Importantly, we find that the strongly constrained and appropriately normed functional yields better accuracy of Em on average, albeit with significant convergence difficulties and notable exceptions of high inaccuracy, while the generalised gradient approximation provides robust qualitative trends in its Em predictions. I will also discuss about the role of uniform background charge and the climbing image approximation in Em predictions.* *In the second part of my talk, I will focus on some of our recent computational screening efforts to discover positive electrodes (cathodes) for Ca-batteries, which are a subset of the multivalent (MV) class of beyond-Li-ion batteries. MV batteries, which typically utilise a metallic anode, can enable systems with higher volumetric energy densities than state-of-the-art Li-ion systems. However, MV batteries require the design of good cathodes that exhibit a high voltage, high capacity, reasonable electroactive ion mobility, and thermodynamic stability. Hence, we screened through the chemical spaces of ternary Ca-containing compounds and Ca-containing polyanionic frameworks as possible Ca-cathodes, using high-through DFT calculations. Importantly, we find a few promising candidates, including vanadium and niobium oxides, and vanadium and manganese phosphates.