  Coulomb breakup of a projectile in the Coulomb field of a fully stripped
heavy nucleus is at present one of the most popular experimental methods to
obtain information on reactions of interest in nuclear astrophysics. Its
theoretical interpretation presents, however, considerable difficulties, due to
the three-body nature and the infinite range of the Coulomb forces involved.
Among the uncertainties affecting present analyses, the possible modification
of the dissociation cross section by three-body Coulomb final-state
interactions plays a major role. Various methods which have been proposed to
deal with it are briefly reviewed. However, none of them is based on a
consistent and mathematically satisfactory quantum mechanical treatment, with
the exception of the one proposed recently. The latter, being based on the
prior form of the dissociation amplitude, makes use of a genuine three-charged
particle wave function for the final state which is an exact solution of the
three-body Schr\"odinger equation, albeit only asymptotically, i.e. for large
distances. Nevertheless, interesting conclusion can be drawn concerning the
influence of three-body Coulomb final-state interactions on quantities of
astrophysical interest.
