  We survey the relationship between the combinatorics and geometry of graphs
and the algebraic structure of right-angled Artin groups. We concentrate on the
defining graph of the right-angled Artin group and on the extension graph
associated to the right-angled Artin group. Additionally, we discuss
connections to geometric group theory and complexity theory. The final version
of this survey will appear in "In the tradition of Thurston, vol.~II",
ed.~K.~Ohshika and A.~Papadopoulos.
