An understanding of interstellar shock waves is crucial in determining the structure of the interstellar medium. By causing the gas to radiate, interstellar shocks provide astronomers with valuable diagnostics on both the physical conditions in the interstellar medium and the energy source that produced the shock. The complexity of the interstellar plasma-its degree of ionization, its molecular content, the presence of small dust grains and cosmic rays, and the magnetic field-leads to a rich variety of structures for interstellar shocks, which are being actively investigated both observationally and theoretically.