  This paper has been prepared by the Symphony collaboration (University of
Warsaw, Uniwersytet Jagiello\'nski, DESY/CNR and ICFO) on the occasion of the
25th anniversary of the "simple man's models" which underlie most of the
phenomena that occur when intense ultrashort laser pulses interact with matter.
The phenomena in question include High-Harmonic Generation, Above-Threshold
Ionization, and Non-Sequential Multielectron Ionization. "Simple man's models"
provide, both an intuitive basis for understanding the numerical solutions of
the time-dependent Schr\"odinger equation, and the motivation for the powerful
analytic approximations generally known as the Strong Field Approximation
(SFA). In this paper we first review the SFA in the form developed by us in the
last 25 years. In this approach SFA is a method to solve the TDSE using a
systematic perturbation theory in a part of the Hamiltonian describing
continuum-continuum transitions in the presence of the laser field. In this
review we focus on recent applications of SFA to HHG, ATI and NSMI from
multi-electron atoms and from multi-atom. The main novel part of the presented
theory concerns generalizations of SFA to: (i) time-dependent treatment of
two-electron atoms, allowing for studies of an interplay between Electron
Impact Ionization (EII) and Resonant Excitation with Subsequent Ionization
(RESI); (ii) time-dependent treatment in the single active electron (SAE)
approximation of "large" molecules and targets which are themselves undergoing
dynamics during the HHG or ATI process. In particular, we formulate the general
expressions for the case of arbitrary molecules, combining input from quantum
chemistry and quantum dynamics. We formulate also theory of time-dependent
separable molecular potentials to model analytically the dynamics of realistic
electronic wave packets for molecules in strong laser fields.
