Classical and quantal nonperturbative treatments of multiphoton and above-threshold ionization

L^2 non-Hermitian Floquet studies of intensity- and frequency-dependent threshold shifts of atomic hydrogen in intense laser fields are presented. We also performed a Monte Carlo classical trajectory study of the motion of an electron under the influence of both the Coulomb and the laser fields. We found that classical results are consistent with quantum-mechanical predictions with regard to continuum threshold shift and above-threshold ionization (ATI). In addition, our classical treatment reveals detailed mechanisms responsible for ATI processes.