Quantum Chromodynamics---the theory of the strong interactions---has the peculiar property that it becomes more strongly coupled as one moves to longer distances. Thus perturbation theory is reliable only at the short distances---or high energies---while a non-perturbative method is needed to describe the low energy phenomena of the theory.
Lattice QCD provides such a method, giving a rigorous, non-perturbative definition of this quantum field theory.
It allows one to calculate quantities such as the ratio of the masses of the rho-meson and nucleon, and the kaon mixing matrix element that leads to CP violation, from first principles using numerical simulations.
Since introduced by Wilson in 1974, the field has steadily progressed, and has now matured into a tool that can calculate a number of quantities to percent-level accuracy, while at the same time giving qualitative insight into phenomena like the confinement of quarks.
Lattice results are poised to play a central role in tests of the flavor sector of the Standard Model of particle physics, and in the search for new physics, in the era of the Large Hadron Collider.
I will describe how lattice QCD is constructed, highlight its successes and challenges, and offer an assessment of the future outlook for this method.