In the last few years, numerical simulations of QCD on the lattice have reached a new level of accuracy. A wide range of thermodynamic quantities is now available in the continuum limit and for physical quark masses. This allows a comparison with measurements from heavy ion collisions for the first time.

Furthermore, calculations of dynamical quantities are also becoming available. The combined effort from first principles and experiment allows to gain an unprecedented understanding of the properties of quark-gluon plasma.

This concise text, geared towards postgraduate students and newcomers to the field, carefully introduces and reviews the state-of-the-art techniques and results from lattice simulations and connects them to the experimental information from RHIC and the LHC.