Fast-paced industrial and agricultural development generates large quantities of hazardous heavy metals (HMs), which are extremely damaging to individuals and the environment. Research in both academia and industry has been spurred by the need for HMs to be removed from water bodies. Advanced materials are being developed to replace existing water purification technologies or to introduce cutting-edge solutions that solve challenges such as cost efficacy, easy production, diverse metal removal, and regenerability. Water treatment industries are increasingly interested in activated carbon because of its high adsorption capacity for HMs adsorption. Furthermore, because of its huge surface area, abundant functional groups on surface, and optimal pore diameter, the modified activated carbon has the potential to be used as an efficient adsorbent. Metal-organic frameworks (MOFs), a novel organic-inorganic hybrid porous materials, sparked an interest in the elimination of HMs via adsorption. This is due to the their highly porous nature, large surface area, abundance of exposed adsorptive sites, and post-synthetic modification (PSM) ability. This review introduces PSM methods for MOFs, chemical modification of activated carbons (ACs), and current advancements in the elimination of Pb2+, Hg2+, and Cd2+ ions from water using modified MOFs and ACs via adsorption.