  Einstein-Maxwell-dilaton theory with non-trivial dilaton potential is known
to admit asymptotically flat and (Anti-)de Sitter charged black hole solutions.
We investigate the conditions for the presence of horizons as function of the
parameters mass $M$, charge $Q$ and dilaton coupling strength $\alpha$. We
observe that there is a value of $\alpha$ which separate two regions, one where
the black hole is Reissner-Nordstr\"om-like from a region where it is
Schwarzschild-like. We find that for de Sitter and small non-vanishing
$\alpha$, the extremal case is not reached by the solution. We also discuss the
attractive or repulsive nature of the leading long distance interaction between
two such black holes, or a test particle and one black hole, from a world-line
effective field theory point of view. Finally, we discuss possible
modifications of the Weak Gravity Conjecture in the presence of both a
dilatonic coupling and a cosmological constant.
