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The properties of hot hadronic matter are of great importance to the studies of heavy-ion collisions, cosmology and compact star formation. I briefly outline the current methods in use in the lattice simulations of QCD thermodynamics at zero and nonzero density. I discuss the most recent results for the QCD phase transition, critical behavior and the equation of state.
We determine the phase diagram of QCD on the mu-T plane for small to moderate chemical potentials. Two transition lines are defined with two quantities, the chiral condensate and the strange quark number susceptibility. The calculations are carried o
We study the phase diagram and the thermodynamic properties of QCD at nonzero isospin asymmetry at physical quark masses with staggered quarks. In particular, continuum results for the phase boundary between the normal and the pion condensation phase
We present results for the topological susceptibility at nonzero temperature obtained from lattice QCD with four dynamical quark flavours. We apply different smoothing methods, including gradient Wilson flow and over--improved cooling, before calcula
We study the phase structure of lattice QCD with heavy quarks at finite temperature and density by a histogram method. We determine the location of the critical point at which the first-order deconfining transition in the heavy-quark limit turns into
Neither the chiral limit nor finite baryon density can be simulated directly in lattice QCD, which severely limits our understanding of the QCD phase diagram. In this review I collect results for the phase structure in an extended parameter space of