  The prediction that black holes radiate due to quantum effects is often
considered one of the most secure in quantum field theory in curved space-time.
Yet this prediction rests on two dubious assumptions: that ordinary physics may
be applied to vacuum fluctuations at energy scales increasing exponentially
without bound; and that quantum-gravitational effects may be neglected. Various
suggestions have been put forward to address these issues: that they might be
explained away by lessons from sonic black hole models; that the prediction is
indeed successfully reproduced by quantum gravity; that the success of the link
provided by the prediction between black holes and thermodynamics justifies the
prediction.
  This paper explains the nature of the difficulties, and reviews the proposals
that have been put forward to deal with them. None of the proposals put forward
can so far be considered to be really successful, and simple dimensional
arguments show that quantum-gravitational effects might well alter the
evaporation process outlined by Hawking. Thus a definitive theoretical
treatment will require an understanding of quantum gravity in at least some
regimes. Until then, no compelling theoretical case for or against radiation by
black holes is likely to be made.
  The possibility that non-radiating "mini" black holes exist should be taken
seriously; such holes could be part of the dark matter in the Universe.
Attempts to place observational limits on the number of "mini" black holes
(independent of the assumption that they radiate) would be most welcome.
