  Molecular self-assembly is a well-known technique to create highly functional
nanostructures on surfaces. Self-assembly on two-dimensional materials is a
developing field and has already resulted in the discovery of several rich and
interesting phenomena. Here, we review this progress with an emphasis on the
electronic properties of the adsorbates and the substrate in well-defined
systems, as unveiled by scanning tunneling microscopy (STM). We cover three
aspects of the self-assembly. The first one focuses on non-covalent
self-assembly dealing with site-selectivity due to inherent moire pattern
present on 2D materials deposited on substrates. Modification of intermolecular
interactions and molecule-substrate interactions influences the assembly
drastically and 2D materials can also be used as a platform to carry out
covalent and metal-coordinated assembly. The second part deals with the
electronic properties of molecules adsorbed on 2D materials. By virtue of being
inert and possessing low density of states near the Fermi level, 2D materials
decouple molecules electronically from the underlying metal substrate and allow
high-resolution spectroscopy and imaging of molecular orbitals. The moire
pattern on the 2D materials causes site-selective gating and charging of
molecules in some cases. The last section covers the effects of self-assembled
organic molecules on the electronic properties of graphene as revealed by
spectroscopy and electrical transport measurements. Non-covalent
functionalization of 2D materials has already been applied for their
application as catalysts and sensors. With the current surge of activity on
building van der Waals heterostructures from 2D materials, molecular
self-assembly has the potential to add an extra level of flexibility and
functionality for applications ranging from flexible electronics and OLEDs to
novel electronic devices and spintronics.
