  The notion of a p-adic de Rham representation of the absolute Galois group of
a p-adic field was introduced about twenty years ago (see e.g. [Fo93]). Three
important results for this theory have been obtained recently: The structure
theorem for the {\it almost $C_p$-representations}, the theorem {\it weakly
admissible implies admissible} and the theorem {\it de Rham implies potentially
semi-stable}. The proofs of the first two theorems are closely related to the
study of a new kind of analytic groups, the {\it Banach-Colmez spaces} and the
proof of the third uses deep results on p-{\it adic differential equations on
the Robba ring}.
