We study a twisted generalization of Novikov algebras, called Hom–Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom–Novikov algebras can be obtained from Novikov algebras by twisting along any algebra endomorphism. All algebra endomorphisms on complex Novikov algebras of dimensions 2 or 3 are computed, and their associated Hom–Novikov algebras are described explicitly. Another class of Hom–Novikov algebras is constructed from Hom-commutative algebras together with a derivation, generalizing a construction due to Dorfman and Gel'fand. Two other classes of Hom–Novikov algebras are constructed from Hom–Lie algebras together with a suitable linear endomorphism, generalizing a construction due to Bai and Meng.