  In the present paper we will investigate the relation between scalar-tensor
theory and $f(R)$ theories of gravity. Such studies have been performed in the
past for the metric formalism of $f(R)$ gravity; here we will consider mainly
the Palatini formalism, where the metric and the connections are treated as
independent quantities. We will try to investigate under which circumstances
$f(R)$ theories of gravity are equivalent to scalar-tensor theory and examine
the implications of this equivalence, when it exists.

General Relativity and Quantum Cosmology;Astrophysics;High Energy Physics - Theory