Solid state electrolytes are promising materials to mitigate the issues derived from the extreme reactivity of the lithium metal anodes in Li-metal batteries. The main properties sought for this application are high ionic conductivity, low electronic conductivity, and high interfacial stability. Here we investigate a class of sulfides (Li10GeP2S12, Li2P2S6, beta-Li3PS4, and Li7P3S11) that have shown relatively good ionic conductivities. However, little is known regarding their interfacial stability. We use density functional theory and ab initio molecular dynamics simulations to investigate the time evolution of the interfacial structure. We characterize atomic diffusion and reactions happening at the picosecond time scale, allowing us to identify the main interfacial products: Li2S, Li3P and Li17Ge4. We then study how the reactivity changes when the Li metal surface is coated with a thin film of Li2S.