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This thesis investigates computational modeling of Li-ion transport in polymer-ceramic composite solid-state electrolytes, organized into three thematic threads which link the research studies into a broader context of scientific development. Firstly, methodological and conceptual advances of force field molecular dynamics (FFMD) techniques are discussed and used to analyse composites of Li₇La₃Zr₂O₁₂ (LLZO) and LiTFSI salt in poly(ethylene oxide) (PEO) materials. The studies address the sensitivity and adequacy of FFMD, temperature dependence and significance of interfacial Li-ion phase exchange, and integration of atomistic insights into a mesoscale framework. This allows the identification of conditions under which interface crossing pathway enhance conductivity in a composite electrolyte as compared to the pure polymer electrolyte. Here, Li-ion phase exchange barrier (PEB) crossing rate, γ_b ~ 3 · 10^-5 ns is calculated at 400 K. Further, the estimated γ_b value is compared to the critical value of the transition rate, above which the conductivity enhancement should result for the ion transport through the ceramic bulk. Moreover, an approach to predict ion diffusivity from potential energy landscape descriptors is demonstrated, enabling a structural basis for screening candidate materials. Secondly, a historical timeline situates the research project within the evolving field of solid-state electrolytes, tracing some selected developments in the understanding of ion transport at the atomistic scale. Thirdly, insights from interviews with six experienced scientists provides a meta-level perspective that examines the meaning, role, and adequacy of models in battery research, highlighting the challenges of interdisciplinary collaboration and the value of integrating diverse methodological approaches. Across these threads, the work demonstrates the significance of atomistic simulations for uncovering interfacial mechanisms inaccessible to direct experiment, while critically assessing their adequacy for predicting macroscopic behavior. Embedded within a multiscale framework, such models prove both sufficient and essential for advancing a broader understanding and improving predictive capability, particularly in the context of electrolyte materials.