The endless introduction of toxic heavy metals through industrialization has worsened the heavy metal pollution in the environment. Thus, the need for its effective removal has become more crucial than before. Studies on graphene-based nanomaterials and their use in removing heavy metals are gaining tremendous traction over the past decade. The properties of graphene oxide (GO), such as large surface areas, desired functional groups and excellent mechanical properties are advantageous. Nevertheless, due to its tendency to agglomerate and difficulty in phase separation after treatment, the functionalization of GO using various materials of different surface functional groups is an ongoing study. The surface modification of GO is done by using various materials to introduce heteroatoms, which have high affinity for heavy metals. This review summarizes the utilization of different surface functional groups, such as oxygen-containing, nitrogen-containing, and sulphur-containing functionalized graphene oxide composites in the adsorption of cationic and oxyanionic heavy metals. The toxicity of these heavy metals is also addressed. Furthermore, the interactions between adsorbents and heavy metals which are influenced by pH and surface functional groups, are also discussed in detail. This is followed by the review in adsorption isotherms and kinetics. Future research needs are also offered.