  We review modified $F(R)$ gravity as realistic candidate to describe the
observable universe expansion history. We show that recent cosmic acceleration,
radiation/matter-dominated epoch and inflation could be realized in the
framework of $F(R)$-gravity in the unified way. For some viable classes of
$F(R)$-gravity, the Newton law is respected and there is no so-called matter
instability (the very heavy positive mass for additional scalar degree of
freedom is generated). The reconstruction program in modified gravity is also
reviewed and it is demonstrated that {\it any} time-evolution of the universe
expansion could be realized in $F(R)$-gravity. These models remain to be
realistic also in the presence of non-minimal gravitational coupling with usual
matter. It is shown that same model which passes local tests and predicts the
unification of inflation with cosmic acceleration also describes dark matter
thanks to presence of additional scalar degree of freedom and chameleon
mechanism.
