<p>We present a high-throughput computational screening for fast lithium-ion conductors to identify promising materials for application in all solid-state electrolytes. Starting from more than 30,000 Li-containing experimental structures sourced from Crystallography Open Database, Inorganic Crystal Structure Database and Materials Platform for Data Science, we perform highly automated calculations to identify electronic insulators. On these ~1000 structures, we use molecular dynamics simulations to estimate Li-ion diffusivities using the pinball model, which describes the potential energy landscape of diffusing lithium with accuracy similar to density functional theory while being 200-500 times faster. Then we study the ~60 most promising and previously unknown fast conductors with full first-principles molecular dynamics simulations at several temperatures to estimate their activation barriers. The MD trajectories of these structures are included along with all the structures on which electronic strutcure calculations were performed. The entire screening provenance is provided for one structure to facilitate the reproduction of this screening.</p>