  We show that f(R)-gravity can, in general, give rise to cosmological viable
models compatible with a matter-dominated epoch evolving into a late
accelerated phase. We discuss the various representations of f(R)-gravity as an
ideal fluid or a scalar-tensor gravity theory, taking into account conformal
transformations. We point out that mathematical equivalence does not
correspond, in several cases, to the physical equivalence of Jordan frame and
Einstein frame. Finally, we show that wide classes of f(R)-gravity models,
including matter and accelerated phases, can be phenomenologically
reconstructed by means of observational data. In principle, any popular
quintessence models could be "reframed" as an f(R)-gravity model.
