  Extending well-known results on surfaces, we give bounds on the cohomological
action of automorphisms of compact K\"ahler threefolds. More precisely, if the
action is virtually unipotent we prove that the norm of $(f^n)^*$ grows at most
as $cn^4$; in the general case, we give a description of the spectrum of $f^*$,
and bounds on the possible conjugates over $\mathbb Q$ of the dynamical degrees
$\lambda_1(f),\lambda_2(f)$. Examples on complex tori show the optimality of
the results.
