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Abstract: Our knowledge about dense matter explored in the cores of neutron stars remains limited. Fortunately, the detection of gravitational waves emitted from the merger of neutron stars and the corresponding electromagnetic signals allow us to place constraints on the properties of matter at supranuclear densities. In this talk, we will combine information from the gravitational-wave signals GW170817 and GW190425, the electromagnetic counterparts AT2017gfo and GRB170817A, with the information provided by NICER and radio pulsar observations to derive new constraints on the neutron-star equation of state and the Hubble constant. In addition to astrophysical observations, extreme densities are probed in terrestrial experiments. We will combine our multi-messenger information with studies from heavy-ion collisions of gold nuclei at relativistic energies with microscopic nuclear theory calculations. Our findings show that constraints from heavy-ion collision experiments show a remarkable consistency with multi-messenger observations and provide complementary information on nuclear matter at intermediate densities.