The anode-free battery has garnered wide attention because of its high theoretical energy density, simplified structure, and minimal costs. Over the past few decades, the successful commercialization of lithium-ion batteries featuring lithium-free anodes-often referred to as "rocking-chair" lithium-ion batteries-has been prominently witnessed worldwide. Aqueous zinc-ion batteries (ZIBs) have attracted extensive interest among researchers for their safety, cost-effectiveness, environmental friendliness, and high ionic conductivity of the electrolyte. Nevertheless, the practical application of ZIBs is predominantly hindered by the dendritic growth of Zn metal anodes, leading to poor cycling stability and potential safety concerns. Therefore, the development of aqueous ZIBs anodes utilizing zinc-free metal materials to replace traditional zinc metal anodes represents a significant advancement. Moreover, comprehensive reviews on this topic are scarce. In this context, we systematically review the emerging Zn-free "rocking-chair" ZIBs (ZFIBs) that employ zinc-based alloy anodes as substitutes for zinc metal anodes. Initially, we introduce the fundamental principles, advantages, and challenges associated with ZFIBs. Subsequently, we provide an overview of the design principles and recent advancements in ZFIBs featuring zinc-free anodes. The review encompasses the progress made in various types of zinc-free anode materials within aqueous ZFIBs, including metals/alloys, metal oxides, metal chalcogenides, MXene materials, organic compounds, in situ solid-electrolyte interphase film stable zinc-free anodes, and other zinc-free anodes. Finally, we offer insights on the future perspectives of "rocking-chair" ZIBs. It is our hope that this paper provides novel strategies for the design and development of zinc-free anodes.