Dark energy problem is considered now as one of the main challenges for XXI century physics. It is quite possible that modified gravity may suggest the gravitational solution for above problem of late-time acceleration of the universe. Simultaneously, modified gravity may describe also the early inflationary universe, thus unifying two accelerating epochs and describing the whole sequence of the universe evolution eras: inflation, radiation/matter dominance and dark energy. Different modified gravities: F(R), F(G), string-inspired scalar-Gauss-Bonnet gravity, non-minimally coupled modified gravities etc. are proposed as models for such early-time and/or late-time accelerating expansion.The current hot topic is devoted to review and to discussion of new results in this approach which gives the gravitational alternative for accelerating expansion, i.e. inflation or dark energy.The idea is very attractive due to fact that according to it, there is no need in the introduction of extra dark components: dark energy, inflaton and/or dark matter. Apart from modified gravity, several works of this issue are devoted to the discussion of dark energy and/or inflation in frames of fluid/scalar theory models.

Motivated by the fact that the pre-inflationary era may evolve in an exotic way, in this work we formalize anisotropic evolution in the context of modified gravity, focusing on pre-inflationary and near the vicinity of the inflationary epochs. We specialize on specific metrics like Bianchi and Taub and we formalize the inflationary theory in vacuum F (R) gravity, in F (R) gravity with an extra scalar field and in Gauss-Bonnet gravity. We discuss the qualitative effects of the anisotropies on the evolution of the Universe and also we consider several specific solutions, like the de Sitter solution, in both the isotropic and anisotropic contexts. Furthermore, several exotic modified gravity cosmological solutions, like the ones which contain finite time singularities, are also discussed in brief.