FAIR next generation scientists - 8th Edition Workshop

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 gravitationnal waves. In this talk, I will review 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.