  We discuss recent developments in the study of primordial black holes,
focussing particularly on their formation and quantum evaporation. Such studies
can place important constraints on models of the early Universe. An especially
interesting development has been the realization that such constraints may be
severely modified if the value of the gravitational "constant" G varies with
cosmological epoch, a possibility which arises in many scenarios for the early
Universe. The nature of the modification depends upon whether the value of $G$
near a black hole maintains the value it had at its formation epoch
(corresponding to gravitational memory) or whether it tracks the background
cosmological value. This is still uncertain but we discuss various approaches
which might help to resolve the issue.
