Numerical simulations of Quantum Chromodynamics on a space-time lattice represent the best non-perturbative tool to explore the QCD phase... Show moreNumerical simulations of Quantum Chromodynamics on a space-time lattice represent the best non-perturbative tool to explore the QCD phase diagram and the behavior of strong interactions under extreme conditions. We review the present status of the field and discuss some recent results. Sponsorship: IIT College of Science, High Energy Physics Division of Argonne National Laboratory Show less