We review recent results obtained for the stripe phases in the Hubbard model. The experimentally observed half-filled (01) stripes with the filling of one hole per two domain wall atoms are stabilized by electron correla- tion effects. We show that the metallic stripe phases obtained using the dynamical mean-field approximation are stabilized by a pseudogap and are qualitatively different from insulating stripes derived from the one-particle (Hartree-Fock) simulations. They reproduce the doping dependence of the size of magnetic domains in (01) stripe phases and agree with the experi- mental data of angle resolved photoemission for La_2-xSr_xCuO_4.
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