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High-order harmonic generation (HHG) is a nonlinear nonperturbative process in ultrashort intense laser-matter interaction. It is the main source of coherent attosecond (1 as = 10−18 s) laser pulses to investigate ultrafast electron dynamics. HHG has become an important table-top source covering a spectral range from infrared to extreme ultraviolet (XUV). One way to extend the cutoff energy of HHG is to increase the intensity of the laser pulses. A consequence of HHG in such intense short laser fields is the characteristic nonadiabatic red and blue shifts of the spectrum, which are reviewed in the present work. An example of this nonperturbative light-matter interaction is presented for the one-electron nonsymmetric molecular ion HeH2+, as molecular systems allow for the study of the laser-molecule orientation dependence of such new effects including a four-step model of MHOHG (Molecular High-order Harmonic Generation).