  Let $p$ be an odd prime number and be an integer coprime to $p$. We survey an
algorithm for computing explicit rational representations of
$(\ell,...,\ell)$-isogenies between Jacobians of hyperelliptic curves of
arbitrary genus over an extension $K$ of the field of $p$-adic numbers
$\mathbb{Q}\_p$. The algorithm has a quasi-linear complexity in $\ell$ as well
as in the genus of the curves.
