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 two or three 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.