  Wiles' work on Fermat's last Theorem highlighted the power of $p$-adic
methods to prove the existence of analytic continuations of $\zeta$ and $L$
functions. These methods have become considerably more sophisticated in recent
years, and have produced a wealth of beautiful results: Hasse--Weil conjecture
for genus $2$ curves, holomorphy of $L$-functions of symmetric powers of
modular forms, etc. We present some of these advances.
