In this talk I will discuss some of my recent results about the possibility of testing compact objects, black-hole alternatives and general relativity with gravitational-wave observations. Currently, these tests are concentrated in searches of deviations from general relativistic predictions in the first and last stage of the gravitational-wave waveform, through the presence of echoes in the post-merger phase and in the late inspiral through quasi-normal modes, multipolar moments, tidal heating and tidal deformability. As a bonus, I will present a new compact star-like object sourced by scalar matter.