  The field of graphene research has developed rapidly since its first
isolation by mechanical exfoliation in 2004. Due to the relativistic Dirac
nature of its charge carriers, graphene is both a promising material for
next-generation electronic devices and a convenient low-energy testbed for
intrinsically high-energy physical phenomena. Both of these research branches
require the facile fabrication of clean graphene devices so as not to obscure
its intrinsic physical properties. Hexagonal boron nitride has emerged as a
promising substrate for graphene devices, as it is insulating, atomically flat
and provides a clean charge environment for the graphene. Additionally, the
interaction between graphene and boron nitride provides a path for the study of
new physical phenomena not present in bare graphene devices. This review
focuses on recent advancements in the study of graphene on hexagonal boron
nitride devices from the perspective of scanning tunneling microscopy with
highlights of some important results from electrical transport measurements.
