  Primordial black holes may form in the early Universe, for example from the
collapse of large amplitude density perturbations predicted in some
inflationary models. Light black holes undergo Hawking evaporation, the energy
injection from which is constrained both at the epoch of nucleosynthesis and at
the present. The failure as yet to unambiguously detect primordial black holes
places important constraints. In this article, we are particularly concerned
with the dependence of these constraints on the model for the complete
cosmological history, from the time of formation to the present. Black holes
presently give the strongest constraint on the spectral index $n$ of density
perturbations, though this constraint does require $n$ to be constant over a
very wide range of scales.
