While the observation of remarkably high ionic conductivities in certain solid materials dates back to Michael Faraday's findings in the 19th century, a comprehensive understanding of the underlying mechanisms responsible for this behavior has continued to elude scientific inquiry. Specifically, the mechanistic details behind the superionic phase transition from a low-ionic conductivity phase to a high-ionic conductivity phase remain poorly understood. This thesis aims to enhance the understanding of these phenomena through theoretical frameworks and simulations. Using recent developments in molecular dynamics, first-principles calculations, and machine learning, the intricate relationship between ionic conductivity and vibrational dynamics
are investigated. First, the thesis reveals that capturing the vibrational dynamics of the superionic transition in Li3N requires a level of phonon theory beyond the harmonic and quasi-harmonic approximations. Then, it confirms some of these insights by simulating an anharmonic general phonon breakdown across the superionic transition from long-timescale machine learning molecular dynamics. Upon further investigation, the simulations reveal that the superionic transition is driven by a decrease in defect formation energy. The thesis finally adopts a big data approach, harnessing existing databases and cutting-edge universal machine learning force fields to test the findings from both this thesis and the literature. Different vibrational descriptors are evaluated against diffusivity, which leads to the discovery of novel fast-ion conductors. Building on the findings from this thesis, the implications for designing vibrational descriptors of ionic conductivity are discussed. Overall, the insights gained from this thesis offer further guidance for the rational design of fast-ion conductors. Thinking beyond the scope of this thesis, the findings may be utilised into high-throughput screening approaches, machine learning models, and inverse design methodologies that can accelerate the development of solid-state batteries.