In Berger's "An introduction to the Theory of $p$-adic Representations", he mentions that due the the equivalence of categories between etale $(\varphi,\Gamma)$-modules and $p$-adic representations, it should be possible to recover **all** properties of $p$-adic representations in terms of $(\varphi,\Gamma)$-modules.

For example, in Herr's 1998 PhD thesis, he shows that the Galois cohomology $H^{i}(-,V)$ of a $p$-adic representation $V$ can be obtained from a complex involving the fixed elements under torsion of the Dieudonne module $\mathbb{D}(V)$.

Since Berger wrote in 2002, which properties do people think can (easily?) be recovered and which have so far?

doesknow how to extract the $\epsilon$-factor -- he just applies the functor which sends the $(\phi,\Gamma)$-module to the corresponding representation and then gets the factor from there. But somehow the underlying premise of the question is that this isn't allowed. – Kevin Buzzard Oct 5 '11 at 10:17