  We determine the asymptotic behavior of the realized power variations, or
more generally of sums of a given test function evaluated at the successive
increments of a L\'{e}vy process. One can completely elucidate the first order
behavior (convergence in probability, possibly after normalization). As for the
associated CLT, one can show some versions of it, but only in a limited number
of cases. In some other cases, a CLT just does not exist.
