Although polycrystalline solid electrolytes are central to the utilization of solid- state batteries with lithium metal anodes, lithium dendrite formation and reduced Li-ion conductivity at their grain boundaries remain primary concerns. Given that experimental studies on polycrystalline materials are notoriously difficult to perform and interpret, computational techniques are invaluable for providing insight at the atomic scale. Here, we carry out first-principles calculations on representative grain boundaries in three important Li-based solid electrolyte families, namely, an anti-perovskite oxide, Li3OCl, a thiophosphate, Li3PS4, and a halide, Li3InCl6, to demonstrate the significantly different impacts that grain boundaries have on their electronic structure, ion conductivity and correlated ion transport. Our results show that even when grain boundaries do not significantly impact ionic conductivity, they can still strongly perturb the electronic structure and contribute to undesirable electrical conductivity and potential lithium dendrite propagation. We also illustrate, for the first time, how cor- related motion, including the so-called paddle-wheel mechanism, which has so far only been considered for the bulk, can vary substantially at grain boundaries. Our findings reveal the dramatically different behaviour of solid electrolytes at the grain boundary compared to the bulk and its potential consequences and benefits for the design of solid-state batteries.