The lattice approximation has proved to be an important technique for studying properties of continuum space-time gauge theories particularly for providing information about the ground state, the low-lying excitations, and thermodynamic behavior. Numerical lattice calculations have given the most convincing evidence to date that quarks are confined in SU(2) and SU(3) Yang-Mills theories, and they promiee to provide values for the masses of the low-lying mesons, baryons, and "glueballs" and to give a thermodynamic description of the theory, without the need for introducing extraneous assumptions about the vacuum state. In principle all we should want to know about the structure of the QCD vacuum and the low-lying states is given by the numerical lattice calculations. We simply need a very large and fast computer. However, most of us find it unsatisfying to characterize the physical vacuum by a set of numbers that only modern mass storage devices can record. Moreover, with present computer facilities it is inconceivable that lattice gauge theories can give detailed information about hadron wave functions, such as, e.g. the charge radius of the neutron. Our ultimate goal should be to obtain approximate analytic models. Nevertheless, the numerical calculations now provide a high standard of comparison according to which any approximate description must be judged.