The analysis of the electronic properties of strained or lattice deformed
graphene combines ideas from classical condensed matter physics, soft matter,
and geometrical aspects of quantum field theory (QFT) in curved spaces. Recent
theoretical and experimental work shows the influence of strains in many
properties of graphene not considered before, such as electronic transport,
spin-orbit coupling, the formation of Moir\'e patterns, optics, ... There is
also significant evidence of anharmonic effects, which can modify the
structural properties of graphene. These phenomena are not restricted to
graphene, and they are being intensively studied in other two dimensional
materials, such as the metallic dichalcogenides. We review here recent
developments related to the role of strains in the structural and electronic
properties of graphene and other two dimensional compounds.Comment: 75 pages, 15 figures, review articl