Zinc-based batteries (e.g., Zn–air, Ag–Zn, Ni–Zn) have the potential to overcome some of the limitations of current Li-ion batteries: safety concerns associated with toxic and flammable electrolytes, high materials/manufacturing costs, and high single-cell specific energy decremented by weight and volume additions to control thermal events in Li-ion stacks. The key to realizing rechargeable aqueous zinc batteries lies in controlling the behavior of the zinc anode during cycling. Our team does this with an architectural redesign of the zinc anode to create an aperiodic monolith of interpenetrating, co-continuous networks of solid and void. Because the architecture ensures three-dimensionally (3D) wiring of all of the transporting reactants (electrons, ions, molecules), the entire volume of the 3D electrode becomes a more uniformly reacting phase, which lowers the kinetics of charge transfer, which minimizes the local current density, which thereby prevents any one region of the zinc electrode launching a dendrite, thereby physically ensuring more uniform charge–discharge reactions. Zinc sponges can now be cycled at high rate, to deep utilization of the *theoretical* zinc capacity, and to a specific energy competitive with lithium-ion batteries in prototype Ag–3D Zn, Ni–3D Zn, and 3D Zn–air cells. The road beyond the drama still too common with Li-based batteries is paved with zinc.