Abstract: Let $p$ be a prime number and let $K$ be a complete discrete valued field of characteristic zero with perfect residue field of characteristic $p$. In order to study $p$-adic representations of $G_K=\mathrm{Gal}(\overline{K}/K)$, Caruso introduced a variant of Fontaine's $(\varphi,\Gamma)$-modules, which he called $(\varphi,\tau)$-modules, replacing the cyclotomic extension in Fontaine's work by a Kummer extension. The overconvergence of étales $(\varphi,\Gamma)$-modules has proven really useful for retrieving invariants and properties of a $p$-adic representation from its $(\varphi,\Gamma)$-modules, and in this talk I will explain how to prove the overconvergence of $(\varphi,\tau)$-modules, following a joint work with Gao. I will then give some applications of this overconvergence, in particular for potentially semi-stable representations.