  The Weak Gravity Conjecture is a nontrivial conjecture about quantum gravity
that makes sharp, falsifiable predictions which can be checked in a broad range
of string theory examples. However, in the presence of massless scalar fields
(moduli), there are (at least) two inequivalent forms of the conjecture, one
based on charge-to-mass ratios and the other based on long-range forces. We
discuss the precise formulations of these two conjectures and the evidence for
them, as well as the implications for black holes and for "strong forms" of the
conjectures. Based on the available evidence, it seems likely that both
conjectures are true, suggesting that there is a stronger criterion which
encompasses both. We discuss one possibility.
