  Kwapie\'{n}'s theorem asserts that every continuous linear operator from
$\ell_{1}$ to $\ell_{p}$ is absolutely $\left( r,1\right) $-summing for
$1/r=1-\left\vert 1/p-1/2\right\vert .$ When $p=2$ it recovers the famous
Grothendieck's theorem. In this paper investigate multilinear variants of these
theorems and related issues. Among other results we present a unified version
of Kwapie\'{n}'s and Grothendieck's results that encompasses the cases of
multiple summing and absolutely summing multilinear operators.
