The Coulomb field of heavy nuclei provides an intense source of quasi-real photons acting on passing nuclear particles. This fact has many applications in studies of problems of nuclear structure and particle physics. In 1984 Coulomb dissociation of fast projectiles was proposed as a novel method to investigate radiative capture processes (time-reversed to photodisintegration). This was a new access to a specific class of radiative capture reactions at low energies, relevant for nuclear astrophysics, and it can overcome various limitations of direct measurements. Since then, various dedicated experiments in this field have been performed and many interesting results have been obtained. The status of this approach is critically reviewed and future directions of experimental and theoretical investigations suggested. After sketching the theoretical basis and the basic experimental requirements, some examples are scrutinized. Emphasis is put on a general discussion of the favourable experimental conditions, of related theoretical problems of the analysis and possible pitfalls of the approach. Various astrophysically relevant cases of current and future applications are discussed.