When an atom or molecule is exposed to a short intense laser pulse, electrons that were removed at an earlier time may be driven back by the oscillating electric field of the laser to recollide with the parent ion, to incur processes like high-order harmonic generation (HHG), high-energy above-threshold ionization (HATI) and nonsequential double ionization (NSDI). Over the years, a rescattering model (the three-step model) has been used to understand these strong field phenomena qualitatively, but not quantitatively. Recently we have established such a quantitative rescattering (QRS) theory. According to QRS, the yields for HHG, HATI and NSDI can be expressed as the product of a returning electron wave packet with various field-free electron-ion scattering cross sections, namely photo-recombination, elastic electron scattering and electron-impact ionization, respectively. The validity of QRS is first demonstrated by comparing with accurate numerical results from solving the time-dependent Schrödinger equation (TDSE) for atoms. It is then applied to atoms and molecules to explain recent experimental data. According to QRS, accurate field-free electron scattering and photoionization cross sections can be obtained from the HATI and HHG spectra, respectively. These cross sections are the conventional tools for studying the structure of a molecule; thus, QRS serves to provide the required theoretical foundation for the self-imaging of a molecule in strong fields by its own electrons. Since infrared lasers of duration of a few femtoseconds are readily available today, these results imply that they are suitable for probing the dynamics of molecules with temporal resolutions of a few femtoseconds.