  We carefully study the $e \rightarrow m$ and $e \rightarrow 0$ limits of the
Reissner-Nordstr\"om spacetime using Geroch's definition of limits of
spacetimes. This is implemented by embedding the one-parameter family of
spacetimes in anti-de Sitter space, and as a result we obtain metrically
correct Penrose diagrams. For $e \rightarrow m$ two distinct limits are
studied.
