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We review on the viability of $F(R)$-gravity. We show that recent cosmicacceleration, radiation/matter-dominated epoch and inflation could be realizedin the framework of $F(R)$-gravity in the unified way. For some classes of$F(R)$-gravity, the correction to the Newton law is extremely small and thereis no so-called matter instability (the very heavy positive mass for additionalscalar degree of freedom is generated). The reconstruction program in modifiedgravity is also reviewed and it is demonstrated that {\it any} time-evolutionof the universe expansion could be realized in $F(R)$-gravity. Specialattention is paid to modified gravity which unifies inflation with cosmicacceleration and passes local tests. It turns out that such a theory maydescribe also dark matter.

Can F(R)-gravity be a viable model: the universal unification scenario for inflation, dark energy and dark matter