Current studies addressing the engineering of charge carrier concentration and the electronic band gap in epitaxial graphene using molecular adsorbates are reviewed. The focus here is on interactions between the graphene surface and the adsorbed molecules, including small gas molecules (H(2)O, H(2), O(2), CO, NO(2), NO, and NH(3)), aromatic, and non-aromatic molecules (F4-TCNQ, PTCDA, TPA, Na-NH(2), An-CH(3), An-Br, Poly (ethylene imine) (PEI), and diazonium salts), and various biomolecules such as peptides, DNA fragments, and other derivatives. This is followed by a discussion on graphene-based gas sensor concepts. In reviewing the studies of the effects of molecular adsorption on graphene, it is evident that the strong manipulation of graphene's electronic structure, including p- and n-doping, is not only possible with molecular adsorbates, but that this approach appears to be superior compared to these exploiting edge effects, local defects, or strain. However, graphene-based gas sensors, albeit feasible because huge adsorbate-induced variations in the relative conductivity are possible, generally suffer from the lack of chemical selectivity.