  Along this review, we focus on the study of several properties of modified
gravity theories, in particular on black-hole solutions and its comparison with
those solutions in General Relativity, and on
Friedmann-Lemaitre-Robertson-Walker metrics. The thermodynamical properties of
fourth order gravity theories are also a subject of this investigation with
special attention on local and global stability of paradigmatic f(R) models. In
addition, we revise some attempts to extend the Cardy-Verlinde formula,
including modified gravity, where a relation between entropy bounds is
obtained. Moreover, a deep study on cosmological singularities, which appear as
a real possibility for some kind of modified gravity theories, is performed,
and the validity of the entropy bounds is studied.
