Equation of State at High-Baryon Density and Compact Stellar Objects

In this contribution I review the connection between compact stars and high-baryon density matter, focusing on astrophysical observables for deconfinement to quark matter. I discuss modern ingredients, repositories, and constraints for the neutron-star equations of state. Finally, I draw comparisons between dense and hot matter created in neutron-star mergers and heavy-ion collisions, and the possibility of quantitatively establishing a link between them.