  Topological defects (e.g. pentagons, heptagons and pentagon-heptagon pairs)
have been widely observed in large scale graphene and have been recognized to
play important roles in tailoring the mechanical and physical properties of
two-dimensional materials in general. Thanks to intensive studies over the past
few years, optimizing properties of graphene through topological design has
become a new and promising direction of research. In this chapter, we review
some of the recent advances in experimental, computational and theoretical
studies on the effects of topological defects on mechanical and physical
properties of graphene and applications of topologically designed graphene. The
discussions cover out-of-plane effects, inverse problems of designing
distributions of topological defects that make a graphene sheet conform to a
targeted three-dimensional surface, grain boundary engineering for graphene
strength, curved graphene for toughness enhancement and applications in
engineering energy materials, multifunctional materials and interactions with
biological systems. Despite the rapid developments in experiments and
simulations, our understanding on the relations between topological defects and
mechanical and physical properties of graphene and other 2D materials is still
in its infancy. The intention here is to draw the attention of the research
community to some of the open questions in this field.
