Einstein’s theory of gravity, General Relativity (GR), has passed all experimental tests so far. Its predictions, such as bending of light near the sun, the perihelion precession of Mercury’s orbit and the existence of gravitational waves have been found in agreement with experiments. One of the pillars for GR is Einstein’s equivalence principle. With the discovery of the accelerated expansion of the Universe, however, questions about new interactions in the dark sector were raised and in some theories the equivalence principle does not hold for dark matter particles (or neutrinos). In this talk I will provide an overview over the motivation of considering such extensions to GR. I will further discuss the current status of such theories in light of cosmological observations and how we can test the predictions of such theories with future cosmological observations.