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Astrophysical Constraints on Strong Modified Gravity

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.