It was Zel'dovich who first clearly realized the importance of quantum vacuum fluctuations in connection with cosmology. Since then, this issue has been more a problem than a solution, even if the acceleration of the universe expansion could, in principle, be easily explained by resorting to it. We have calculated those contributions in a number of different models. Under some specific conditions, the results look promising, although a general acceptable solution looks still far from reach. © 2008 EAS EDP Sciences.