With exceptional carrier mobilities, mechanical strength, and optical transparency, graphene is a leading material for next-generation electronic devices. However, for most applications, graphene will need to be integrated with other materials, which motivates efforts to understand and tune its surface chemistry. In particular, the modification of graphene via organic functionalization holds promise for tuning the electronic properties of graphene, controlling interfaces with other materials, and tailoring surface chemical reactivity. Toward these ends, this article reviews recent work from our laboratory on noncovalent and covalent organic functionalization of graphene. Using ultrahigh vacuum scanning tunneling microscopy (UHV STM), the molecular ordering and electronic properties of organic adlayers on graphene are characterized at the molecular scale. In addition, UHV STM is employed to nanopattern these organic layers with sub-5 nm resolution, thus providing a pathway for producing graphene-based heteromolecular nanostructures.