Breakup reactions are generally quite complicated, they involve nuclear and electromagnetic forces including interference effects. Coulomb dissociation is an especially simple and important mechanism since the perturbation due to the electric field of the nucleus is exactly known. Therefore firm conclusions can be drawn from such measurements. Electromagnetic matrixelements, radiative capture cross-sections and astrophysical S-factors can be extracted from experiments. We describe the basic theory, give analytical results for higher order effects in the dissociation of neutron halo nuclei and briefly review the experimental results obtained up to now. Some new applications of Coulomb dissociation for nuclear astrophysics and nuclear structure physics are discussed.