  This paper follows the inaugural talk one of the authors (LT) gave at the
opening of the ECT* workshop with the same title, which he co-organized in
Trento, Italy, November 5-9, 2018. As such it follows the ideas expressed
there, which were to out-line the discussions that the organizers intended for
that meeting. Therefore, the paper will review the indirect methods in nuclear
astrophysics, their use and their specific problems, old and new, the need to
further developments rather than giving complete treatments of each method or
reviewing exhaustively the existing literature. The workshop was from its
inception aiming also at reviewing the status of the field of nuclear
astrophysics and its connections with adjacent branches of physics. Some lines
on these are included here.
