  The aim of this paper is to give a survey of nonassociative Hom-algebra and
Hom-superalgebra structures. The main feature of these algebras is that the
identities defining the structures are twisted by homomorphisms. We discuss
Hom-associative algebras, Hom-Flexible algebras, Hom-Lie algebras,
$G$-hom-associative algebras, Hom-Poisson algebras, Hom-alternative algebras
and Hom-Jordan algebras and $\mathbb{Z}_2$-graded versions. We give an overview
of the development of Hom-algebras structures which have been intensively
investigated recently.
