  Starting from the weak field limit, we discuss astrophysical applications of
Extended Theories of Gravity where higher order curvature invariants and scalar
fields are considered by generalizing the Hilbert-Einstein action linear in the
Ricci curvature scalar $R$. Results are compared to General Relativity in the
hypothesis that Dark Matter contributions to the dynamics can be neglected
thanks to modified gravity. In particular, we consider stellar hydrostatic
equilibrium, galactic rotation curves, and gravitational lensing. Finally, we
discuss the weak field limit in the Jordan and Einstein frames pointing out how
effective quantities, as gravitational potentials, transform from one frame to
the other and the interpretation of results can completely change accordingly.
