Rechargeable Li-metal batteries using high-voltage cathodes can deliver the highest possible energy densities among all electrochemistries. However, the notorious reactivity of metallic lithium as well as the catalytic nature of high-voltage cathode materials largely prevents their practical application. Here, we report a non-flammable fluorinated electrolyte that supports the most aggressive and high-voltage cathodes in a Li-metal battery. Our battery shows high cycling stability, as evidenced by the efficiencies for Li-metal plating/stripping (99.2%) for a 5 V cathode LiCoPO4 (-99.81%) and a Ni-rich LiNi0.8Mn0.1,Co-0.3,O-2 cathode (-99.93%). At a loading of 2.0 mAh cm(-2), our full cells retain -93% of their original capacities after 1,000 cycles. Surface analyses and quantum chemistry calculations show that stabilization of these aggressive chemistries at extreme potentials is due to the formation of a several-nanometre-thick fluorinated interphase.