The “Facility for Antiproton and Ion Research” (FAIR) in Darmstadt, Germany, and the “Nuclotron-based Ion Collider Facility” (NICA) in Dubna, Russia, are two accelerator centers under construction. FAIR will provide beams and experimental setups to perform forefront research in hadron, nuclear, atomic, and plasma physics, as well as in radiation biology and material science. At NICA, a unique research program on nuclear matter and spin physics will be conducted. Both facilities will execute experiments to explore the properties of QCD matter at neutron star core densities, in order to study the high-density equation of state, and to shed light on the quark degrees-of-freedom emerging in QCD matter at high densities. The research programs will be performed at FAIR with the CBM experiment, and at NICA with the MPD setup at the collider, and with the BM@N experiment at the Nuclotron. These three experiments are complementary, with respect to the beam energy. The physics programs and the relevant experimental observables will be discussed.