The Cauchy problem for f(R)-gravity: an overview

We review the Cauchy problem for f® theories of gravity, in metric and metric-affine for- mulations, pointing out analogies and differences with respect to General Relativity. The role of conformal transformations, effective scalar fields and sources in the field equations is discussed in view of the well-posedness of the problem. Finally, criteria of viability of the f®-models are considered according to the various matter fields acting as sources.