The detection of the GW170817 neutron star merger event has incited an intense research activity towards the understanding of the nuclear matter equation of state. In this paper we compare in particular the pressure-density relation obtained from heavy-ion collisions with the analysis of the NS merger event. Moreover, we present recent calculations of neutron stars moment of inertia and tidal deformability using various microscopic equations of state for nuclear and hybrid star configurations, and confirm several universal relations. We also discuss the recent constraints for the NS radii determined by GW170817, and find compatible radii between 12 and 13 kilometers, thus identifying the suitable equations of state.
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