The recent almost coincidental detection of gravitational waves and gamma rays burst by the LIGO-VIRGO network and satellite collaborations, and interpreted as the coalescence of a binary neutron star system, has caused a slaughter of the many extensions of Einstein’s General Theory of Relativity. Such extensions are aimed to resolve several problems, such as the dark matter/dark energy issue, or the existence of singularities deep inside black holes and in the early Universe. In this talk I will introduce a family of Ricci-based metric-affine theories which are compatible with the observations made by LIGO-VIRGO so far. I will thus introduce a taxonomy of the different compact objects found in these theories and how they may contribute to the resolution of spacetime singularities, their astrophysical interpretations, and the understanding of gravitational waves.