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The propensity of metals to form irregular and nonplanar electrodeposits at liquid-solid interfaces has emerged as a fundamental barrier to high-energy, rechargeable batteries that use metal anodes. We report an epitaxial mechanism to regulate nucleation, growth, and reversibility of metal anodes. The crystallographic, surface texturing, and electrochemical criteria for reversible epitaxial electrodeposition of metals are defined and their effectiveness demonstrated by using zinc (Zn), a safe, low-cost, and energy-dense battery anode material. Graphene, with a low lattice mismatch for Zn, is shown to be effective in driving deposition of Zn with a locked crystallographic orientation relation. The resultant epitaxial Zn anodes achieve exceptional reversibility over thousands of cycles at moderate and high rates. Reversible electrochemical epitaxy of metals provides a general pathway toward energy-dense batteries with high reversibility.