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Numerical simulations have become an important tool to understand and predict nonperturbative phenomena in particle physics. We attempt to present a general overview over the field. First, the basic concepts of lattice gauge theories are described, including a discussion of currently used algorithms and the reconstruction of continuum physics from lattice data. We then proceed to present some results for QCD, both at low energies and at high temperatures, as well as for the electro-weak sector of the standard model.