We begin with a brief review of the ionization of 3D hydrogen atoms with large principal quantum number n0, first by a static electric field Fs and then by linearly polarized (LP) electric field. Near its onset, LP ionization can be understood with (1D + time) theory. Various kinds of resonant phenomena are important. We continue with a brief review of the polarization dependence. When the dynamics is dominated by the main pendulum-like resonance zone, a separation of timescales leads to ionization near onset that is independent of polarization. In other parameter ranges, polarization-dependent effects occur that can be understood only in higher dimensions, minimally (2D + time). Finally, we present preliminary results from new experiments using collinear LP and Fs fields, both of which can be strong. The data show the importance of (a) multiphoton resonances driven between Stark substates of the initial n0 manifold and (b) striking, regular oscillations recorded for fixed microwave parameters as a function of Fs. The mechanisms responsible for (a) are understood. Those responsible for (b) are not, but the oscillations exhibit empirical scaling behavior that will help to unravel the wave packet dynamics. © 1999 Published by Elsevier Science B.V. All rights reserved.