  An inflationary stage dominated by a $D$-term avoids the slow-roll problem of
inflation in supergravity and may emerge in theories with a non-anomalous or
anomalous U(1) gauge symmetry. The most intriguing and commonly invoked
possibility is that the Fayet-Iliopoulos $D$-term triggering inflation is the
one emerging in superstring theories. We discuss the complications one has to
face when trying to build up a successful $D$-term inflationary scenario in
superstring models. In particular, we show that the ``vacuum shifting''
phenomenon of string theories is usually very efficient even in the early
Universe, thus preventing inflation from taking place. On the other hand, when
$D$-term inflation is free to occur, the presence of a plethora of fields and
several non-anomalous additional abelian symmetries in string theories may help
in reconciling the value of the Fayet-Iliopoulos $D$-term required by the COBE
normalization with the value predicted by string theories. We also show that in
superstring $D$-term inflation gravitinos are likely to pose no cosmological
problem.
