  This is a 20-year old review on singularities and singularity theorems. The
main reason to submit it now is -apart from increasing its availability- to
correct a very strange error that appears in the journal's online version: it
contains wrong headers and footers in its 1st page. This has led to many wrong
citations, and to some confusion. The pdf file here contains the right
information.
  ORIGINAL ABSTRACT: A detailed study of the singularity theorems is presented.
I discuss the plausibility and reasonability of their hypotheses, the
applicability and implications of the theorems, as well as the theorems
themselves. The consequences usually extracted from them, some of them without
the necessary rigour, are widely and carefully analysed with many clarifying
examples and alternative views.
