The high densities achieved in neutron stars and the high densities and temperatures achieved 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 directly observed. New electromagnetic and gravitational-wave constraints have been slowly constraining the dense QCD equation of state, allowing us to learn important information about the strong interaction. Nevertheless, strong constraints on dense and hot matter depend on (a) the not yet observed post-merger period of gravitational-wave production from neutron-star mergers and (b) non-trivial comparisons with particle collision experimental data. In this talk, I discuss where we stand and what we expect to learn about dense matter in the near future.