We present a computational screening of experimental structural repositories for fast Li-ion conductors, with the goal of finding new candidate materials for application as solid-state electrolytes in next-generation batteries. We start from ∼1400 unique Licontaining materials, of which ∼900 are insulators at the level of density-functional theory. For those, we calculate the diffusion coefficient in a highly automated fashion, using extensive molecular dynamics simulations on a potential energy surface (the recently published pinball model) fitted on first-principles forces. The ∼130 most promising candidates are studied with full first-principles molecular dynamics, first at high temperature and then more extensively for the 78 most promising candidates. The results of the first-principles simulations of the candidate solid-state electrolytes found are discussed in detail.of superionic conductors is the recent discovery of Li-argyrodites [22], with the general formula Li 7 PS 5 X (X=Cl, Br, I) or Li 7 PS 6 (sulphur can be replaced with oxygen, but this reduces the ionic conductivity [23]). Third, Li-containing NASICONs (sodium superionic conductors) are phosphates with the structural formula Li 1+6x X 4+2−x Y 3+x (PO