The study of the nuclear matter equation-of-state (EoS) is a relevant topic of modern nuclear physics. It governs the behaviour of nuclear matter away from the normal conditions found in nuclei interiors and plays a major role in heavy-ion collisions, in determining neutron skin thicknesses of neutron rich nuclei and the mass-radius relation of neutron stars, and in modelizations of supernovae explosions. Its uncertain knowledge is related to difficulties in solving the many-body problem with realistic nuclear interactions. In the last decades several studies, from both theoretical and experimental sides, have allowed relevant progress in the description of the EoS, both for the isospin-symmetric matter and for the isospin-asymmetric matter, the so called symmetry energy, especially at densities below the saturation point. In this paper we review some of the studies on the high-density behavior of the EoS, obtained by studying heavy-ion collisions with incident energies between several hundred MeV up to about 2 GeV per nucleon, with a focus on those carried out at the GSI laboratory in Darmstadt (Germany) by using the SIS18 accelerator beams. Constraints on the isospin-symmetric matter