  We survey results on the pebbling numbers of graphs as well as their
historical connection with a number-theoretic question of Erd\H os and Lemke.
We also present new results on two probabilistic pebbling considerations, first
the random graph threshold for the property that the pebbling number of a graph
equals its number of vertices, and second the pebbling threshold function for
various natural graph sequences. Finally, we relate the question of the
existence of pebbling thresholds to a strengthening of the normal property of
posets, and show that the multiset lattice is not supernormal.
