The comprehension of several essential aspects of strong interactions and of the Standard Model requires a treatment of Quantum Chromodynamics (QCD), the theory of quarks and gluons, at a non-perturbative level, leaving important issues still open.
The discretization of QCD on a space-time lattice, first proposed by K.G. Wilson, provides the ideal framework for a numerical non-perturbative computation of the theory starting from first principles.
In this talk, I will review the progress achieved in this way towards the understanding of the observed properties of hadronic matter and the prediction of new properties of strongly interacting matter in presence of unusual conditions, reproducible in heavy ion experiments and in astrophysical and cosmological contexts.
