  Recently a class of alternative theories of gravity which goes under the name
f(R) gravity, has received considerable attention, mainly due to its
interesting applications in cosmology. However, the phenomenology of such
theories is not only relevant to cosmological scales, especially when it is
treated within the framework of the so called Palatini variation, an
independent variation with respect to the metric and the connection, which is
not considered a priori to be the Levi-Civita connection of the metric. If this
connection has its standard geometrical meaning the resulting theory will be a
metric-affine theory of gravity, as will be discussed in this talk. The general
formalism will be presented and several aspects of the theory will be covered,
mainly focusing on the enriched phenomenology that such theories exhibit with
respect to General Relativity, relevant not only to large scales (cosmology)
but also to small scales (e.g. torsion).
