Prospects for constraining phase transition scenarios with neutron stars

In the past several years multifarious new data from gravitational wave detectors, X-ray satellites, and nuclear experiments have become available with increasingly better accuracy which greatly improved the understanding of neutron-star physics. In this talk, I will discuss what we have learned about the equation of state for strongly-interacting matter at supra-nuclear densities using astronomical and terrestrial probes, as well as advances in theory and modeling efforts needed to interpret these observations. In particular I will focus on recent development in constraining viable scenarios of possible phase transitions in the dense interior of neutron stars. Of great interest for nuclear and particle physics, neutron stars are at the heart of multimessenger astronomy to address longstanding puzzles about how matter behaves under the most extreme conditions in our Universe.