The review is devoted to new effects discovered recently in the course of studying the process of nonlinear ionization of atoms in the field of laser radiation--above-threshold ionization, manifestation of multielectron structure of complex atoms, formation of multiply charged ions, tunneling ionization, and emission of short-wavelength radiation. The main experimental data and their theoretical interpretation are presented. A discussion is given of the criteria for the applicability of the lowest non-vanishing order of non-steady-state perturbation theory to the description of the interaction of an atom with the electromagnetic field.