  We review the current methods and results of lattice simulations of quantum
chromodynamics at nonzero temperatures and densities. The review is intended to
introduce the subject to interested nonspecialists and beginners. It includes a
brief overview of lattice gauge theory, a discussion of the determination of
the crossover temperature, the QCD phase diagram at zero and nonzero densities,
the equation of state, some in-medium properties of hadrons including
charmonium, and some plasma transport coefficients.
