Heavy metal contamination in soil and water has become a serious threat to all forms of life. Finding a sustainable remediation method is the prime concern of researchers worldwide. In this quest, cellulose has emerged as a biocompatible, biodegradable, renewable, tunable, and cost-effective bioadsorbent for heavy metal removal from polluted water. Cellulose is rich in hydroxyl groups which can be chemically modified to enhance the reactivity, binding sites, and mechanical strength. Cellulose in nano size, i.e., nanofibers and nanocrystals, offer myriad opportunities to improve the aspect ratio, surface area, pore size, and hydrophilicity for effective adsorption. In this review, chemical and physical modifications in cellulose (functional group transformations, nanocellulose, nanocomposites, hydrogels, aerogels, beads, and membranes) with respect to adsorption of divalent heavy metal ions, in particular, Pb2+, Cu2+, and Cd2+, have been extensively discussed. This review also examines the effect of pH, concentration, temperature, and contact time on the adsorption process. Different mechanisms for heavy metal removal such as ion exchange, electrostatic interactions, complexation, chelation, precipitation, and reduction have been discussed. Theoretical insights into the mechanisms of adsorbent–adsorbate binding are critically examined in the context of modified cellulose. The authors, in the concluding section, summarize potential research directions toward developing sustainable biosorbents.