Charge/discharge rates and low-temperature performance of metal-ion batteries are strongly affected by the ionic conductivity of transition metal intercalation materials used in electrodes.  Computational methods, based on crystal chemistry empirical approaches and rigorous density functional theory have become indispensable for the evaluation of ionic conductivity in such materials. During the last decade, hundreds of computational studies of various intercalation materials accumulated considerable knowledge regarding ionic conductivity. This review covers the modern crystal chemistry methods and their application to transition metal intercalation materials, as well as systematizes the available information retrieved from mostly density functional theory studies related to mechanisms of ionic conductivity/diffusivity with the focus on elementary migration acts of alkali cations. We consider in detail how the diffusion channel size and dimension, coordination, cation size, anion and transition metal type, oxidation state, state of charge/discharge, and other factors affect elementary migration acts of alkali cations. The review collects the design principles of new intercalation materials with high ionic conductivity being helpful for advanced energy storage technologies development.