  We offer a discussion on the strong field regime predictions of two families
of theories that deviate from General Relativity in different aspects:
$f(R)$-gravity and Scalar-Tensor-Vector Gravity (STVG). We discuss
astrophysical effects in models based upon both matter and vacuum solutions of
such theories. In particular, we analize neutron star structure and the
constraints on the parameters of the theories introduced by the latest
observations. We also review black hole solutions and several astrophysical
consequences of them, including accretion disks and jets. Finally, we report on
the implications of the detection of various gravitational wave events for
these theories.
