Multi-valent (MV) ion intercalation batteries that replace Li+ ions with MV cations such as Mg2+, Zn2+ and Ca2+ constitute a promising strategy to meet the energy density requirements of the next generation of electrical devices. One of the most pressing obstacles to the development of high-energy density MV-ion systems is the discovery of cathode materials offering sufficiently high voltage and, most importantly, high MV cation mobility. To date, there have only been a limited number of examples demonstrating the feasibility of rechargeable multivalent batteries, with most of the focus placed on Mg-cycling. Thus, it is important to assess the feasibility of several chemical spaces as multivalent intercalation cathodes. We will present a detailed analysis, based on first-principles DFT calculations, of multivalent ion intercalation in various promising candidates such as the spinel AnB2X4 (A = MV as Mg, Zn or Ca, B = transition metal and X = O2- or S2-), olivine AnFePO4 and various vanadium pentoxide AnV2O5 polymorphs [1-5]. Emphasis will be given to host structures exhibiting enhanced Mg or Zn mobility, and in particular to the chemical and structural descriptors which govern this property. Our findings show that matching the MV site preference to the diffusion topology of the host controls the ionic mobility, more significantly than any other factor, providing design guidelines to find fast-diffusing MV conductors. For example, Zn ions are expected to diffuse well in hosts where Zn ions are in non-preferred but stable octahedral sites and migrate through favored unstable tetrahedral site. We will also show some experimental data that validates these design rules. The results demonstrate that computational materials science is a powerful tool to enable the successful development and optimization of new materials for energy dense multivalent batteries. The work is entirely supported by the Department of Energy as part of the Joint Center for Energy Storage Research (JCESR). [1] Z. Rong, R. Malik, P. Canepa, G. Gautam, M. Liu, A. Jain, K. Persson and G. Ceder, Materials Design Rules for Multi-Valent Ion Mobility in Intercalation Structures, Chem. Mat. 2015, 27, 6016. [2] M. Liu, Z. Rong, R. Malik, P. Canepa, A. Jain, G. Ceder and K. Persson, Spinel compounds as multivalent battery cathodes: a systematic evaluation based on ab initio calculations, Energy Environ. Sci. 2015, 8, 964. [3] G. Gautam, P. Canepa, A. Abdellahi, A. Urban, R. Malik and G. Ceder, Intercalation phase diagram of Mg in V2O5 from first principles, Chem. Mat. 2015, 27, 3733. [4] G. Gautam, P. Canepa, R. Malik, M. Liu, K. Persson and G. Ceder, First-principles evaluation of multi-valent cation insertion into orthorhombic V2O5, Chem. Comm. 2015, 51, 13619. [5] G. Gautam, P. Canepa, W. D. Richards, R. Malik and G. Ceder, Role of structural H2O in intercalation electrodes: the case of Mg in Nanocrystalline Xerogel-V2O5, Nano. Lett. 2016, 16, 2426–2431.