  The aim of this paper is that of discussing Closed Graph Theorems for
bornological vector spaces in a way which is accessible to non-experts. We will
see how to easily adapt classical arguments of functional analysis over
$\mathbb{R}$ and $\mathbb{C}$ to deduce Closed Graph Theorems for bornological
vector spaces over any complete, non-trivially valued field, hence encompassing
the non-Archimedean case too. We will end this survey by discussing some
applications. In particular, we will prove de Wilde's Theorem for
non-Archimedean locally convex spaces and then deduce some results about the
automatic boundedness of algebra morphisms for a class of bornological algebras
of interest in analytic geometry, both Archimedean (complex analytic geometry)
and non-Archimedean.
