  Graphene, the one-atom-thick sp2 hybridized carbon crystal, displays unique
electronic, structural and mechanical properties, which promise a large number
of interesting applications in diverse high tech fields. Many of these
applications require its functionalization, e.g. with substitution of carbon
atoms or adhesion of chemical species, creation of defects, modification of
structure of morphology, to open electronic band gap to use it in electronics,
or to create 3D frameworks for volumetric applications. Understanding the
morphology-properties relationship is the first step to efficiently
functionalize graphene. Therefore a great theoretical effort has been recently
devoted to model graphene in different conditions and with different approaches
involving different level of accuracy and resolution. Here we review the
modeling approaches to graphene systems, with a special focus on atomistic
level methods, but extending our analysis onto coarser scales. We illustrate
the methods by means of applications with possible potential impact.
