Non-Li metal-ion rechargeable battery systems, e.g., Na-, K-, Mg-, and Ca-ion systems, are at the brink of playing a major role for sustainable energy and grid storage, in part owing to their significant availability as compared to Li-ion rechargeable systems. However, non-Li-based systems pose their own unique set of challenges: the large ionic size of the respective ions especially for Na and K systems, weak kinetics, and low-voltage window of Mg-ion systems, etc., which prevent efficient reversibility. Developing efficient electrode materials with novel morphologies is one of the main ways to harness the potential on the non-Li-ion systems. It is here that two-dimensional (2D) layered materials which have excellent structural, electrochemical, and mechanical properties can be considered to be prime candidates for negative electrode materials in non-Li-based energy storage systems. Therefore, research in the various aspects of 2D materials encompassing their fabrication techniques, tailoring their morphology, and application as anodes in non-Li systems has significantly increased in recent years, with more expected increase in the future. With this perspective in mind, here we provide an exhaustive review of the structure and properties of various 2D materials (graphene, phosphorene, and transition metal dichalcogenides), their performances as anode materials in emerging non-Li-based energy storage systems, and the obstacles that must be overcome at each stage.