Can Deconfinement Occur in Neutron Stars?

The large density reached in neutron stars and the large density and temperature reached in neutron-star mergers create ideal testing grounds in which to learn about exotic matter, namely hyperons and deconfined quarks. The presence of exotic matter can strongly affect the interior of neutron stars but cannot be easily observed. New electromagnetic and gravitational-wave constraints have been slowly narrowing down the dense and cold equation of state and allowing us to learn more about the strong interaction. Nevertheless, constraints on dense and hot matter depend on the not yet observed post-merger portion of gravitational waves from neutron-star mergers and non-trivial comparisons with particle collisions in the laboratory. In this talk, I address these issues, giving special attention to possible constraints coming from extremely massive neutron stars.