  We briefly review f(R) theories, both in the metric and Palatini
formulations, their scalar-tensor representations and the chameleon mechanism
that could explain the absence of perceptible consequences in the Solar System.
We also review f(T) theories, a different approach to modified gravity
consisting in a deformation of the teleparallel equivalent of General
Relativity. We show some applications to cosmology and cosmic strings. As
f(R)'s, f(T) theories are not exempted from additional degrees of freedom; we
also discuss this still open issue.
