Graphene, a one-atom-thick sp2-hybridized carbon sheet, has enormous potential for fabricating flexible transparent electronics due to its unique electronic and mechanical properties. However, the intrinsic lack of a band gap, the low reactivity, and the poor solubility of pristine graphene have largely hindered wide-ranging applications so far. One of the most attractive ways to resolve these issues is to modify the graphene surface through molecular physisorption or chemisorption. In this review, we summarize the recent progress in fabricating graphene-based molecular electronics through manipulating small functional molecules on the graphene surface towards chemical reactivity adjustment, molecular doping, and band gap opening via non-covalent and covalent interactions, and draw attention to challenges and opportunities. We also suggest future research directions for graphene-based molecular electronics.