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.
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