  We review results from lattice QCD calculations on the thermodynamics of
strong-interaction matter with emphasis on input these calculations can provide
to the exploration of the phase diagram and properties of hot and dense matter
created in heavy ion experiments. This review is organized as follows: 1)
Introduction, 2) QCD thermodynamics on the lattice, 3) QCD phase diagram at
high temperature, 4) Bulk thermodynamics, 5) Fluctuations of conserved charges,
6) Transport properties, 7) Open heavy flavors and heavy quarkonia, 8) QCD in
external magnetic fields, 9) Summary.
