The phase diagram of nuclear matter is one the most fundamental pieces of knowledge in modern
physics, reflecting how QCD governs the thermodynamics of matter under extreme conditions.
Not only related to the understanding of the early Universe, or used to describe the evolution of the
system created in relativistic heavy-ion collisions, it has gained even more insights in the past years
through the observation of neutron star mergers with gravitational waves. I review succinctly here
the main theories, models and approaches used to explore this phase diagram at finite temperature
and densities, as well as the most recent updates in this regard.