Reversible intercalation of guest ions in graphite is the key feature utilized in modern battery technology. In particular, the capability of Li-ion insertion into graphite enabled the successful launch of commercial Li-ion batteries 30 years ago. On the road to explore graphite as a universal anode for post Li-ion batteries, the conventional intercalation chemistry is being revisited, and recent findings indicate that an alternative intercalation chemistry involving the insertion of solvated ions, designated as co-intercalation, could overcome some of the obstacles presented by the conventional intercalation of graphite. As an example, the intercalation of Na ions into graphite for Na-ion batteries has been perceived as being thermodynamically impossible; however, recent work has revealed that a large amount of Na ions can be reversibly inserted in graphite through solvated-Na-ion co-intercalation reactions. More recently, it has been extensively demonstrated that with appropriate electrolyte selection, not only Na ions but also other ions such as Li, K, Mg, and Ca ions can be co-intercalated into a graphite electrode, resulting in high capacities and power capabilities. The co-intercalation reaction shares a lot in common with the conventional intercalation chemistry but also differs in many respects, which has attracted tremendous research efforts in terms of both fundamentals and practical applications. Herein, we aim to review the progress made in understanding the solvated-ion intercalation mechanisms in graphite and to comprehensively summarize the state-of-the-art achievements by surveying the correlations among the guest ions, co-intercalation conditions, and electrochemical performance of batteries. In addition, the advantages and challenges related to the practical application of graphite undergoing co-intercalation reactions are presented.