Lattice QCD at finite temperature and density

Abstract

I review recent lattice results on strongly interacting matter under extreme conditions, with emphasis on the finite-temperature QCD transition at ${\mu }_B=0$, its approach toward the chiral limit and the fate of the $U_A(1)$ anomaly, as well as recent constraints on the QCD phase boundary and the possible critical endpoint at ${\mu }_B>0$. I also discuss selected advances in lattice methods and in QCD thermodynamics under external conditions, in particular strong magnetic fields, isospin chemical potential, rotation, acceleration, and quark spin polarization.

Comments: 24 pages, 10 figures, plenary talk presented at the 42nd International Symposium on Lattice Field Theory (Lattice 2025), 2-8 November 2025, Mumbai, India; version in PoS