  Let $X$ be a real L\'evy process and let $\Xpos $ be the process conditioned
to stay positive. We assume that $ 0 $ is regular for $(-\infty, 0)$ and $(0,
+\infty) $ with respect to $X$. Using elementary excursion theory arguments, we
provide a simple probabilistic description of the reversed paths of $X$ and
$\Xpos $ at their first hitting time of $ (x, +\infty)$ and last passage time
of $ (-\infty, x ] $, on a fixed time interval $[0, t]$, for a positive level
$x$. From these reversion formulas, we derive an extension to general L\'evy
processes of Williams' decomposition theorems, Bismut's decomposition of the
excursion above the infimum and also several relations involving the reversed
excursion under the maximum.
