Rechargeable zinc-ion batteries (ZIBs) are promising for large scale energy storage and portable electronic applications due to their low cost, material abundance, high safety, acceptable energy density and environmental friendliness. This tutorial review presents an introduction to the fundamentals, challenges, recent advances and prospects related to ZIBs. Firstly, the intrinsic chemical properties, challenges and strategies of metallic zinc anodes are underscored. Then, the multiple types of cathode materials are classified and comparatively discussed in terms of their structural and electrochemical properties, issues and remedies. Specific attention is paid to the mechanistic understanding and structural transformation of cathode materials based on Zn ion-(de)intercalation chemistry. After that, the widely investigated electrolytes are elaborated by discussing their effect on Zn plating/stripping behaviours, reaction kinetics, electrode/electrolyte interface chemistries, and cell performances. Finally, the remaining challenges and future perspectives are outlined for the development of ZIBs.