Composite polyethylene-oxide/garnet electrolytes containing LiTFSI as the lithium salt have a Li+ conductivity σLi > 10−4 Scm−1 at 55°C and a low plating/stripping impedance of a dendrite-free Li-metal anode; they have been developed for a safe solid-state Li-metal rechargeable battery. Composites consisting of “ceramic-in-polymer” to “polymer-in-ceramic” that are flexible and mechanically robust are fabricated by hot-pressing. Safe pouch cells with a remarkable flexibility have been fabricated. Solid-state LiFePO4 |Li batteries with electrolytes of “ceramic-in-polymer” and “polymer-in-ceramic” deliver excellent cycling stability with high discharge capacities (139.1mAhg–1 with capacity retention of 93.6% after 100 cycles) and high capacity retention (103.6% with coulombic efficiency of 100% after 50 cycles) at 0.2C and 55°C. Both kinds of electrolytes can be applied to solid-state lithium batteries.