In this account of open problems in the field of atom-laser physics at very high field intensities, we have focused the discussion on the questions raised by the results reported in recent experiments on multiple ionization of a rare gas in ultrastrong laser fields. In order to address these questions, we present the results of a set of simulations based on the numerical solution of the time-dependent Schrodinger (and/or Klein-Gordon) equation for simple one-dimensional models of atoms and ions.