When diatomic and triatomic molecules are exposed to subpicosecond laser pulses (focused intensities well in excess of 1014W cm−2; wavelengths of the order 600 nm), they are highly ionized. The laser electric fields are so large that they compete with, and in some cases exceed, the internal fields binding the valence electrons. The result is that conventional perturbation theory is inapplicable and one has to resort to alternative approaches. A simple starting point is the field ionization, Coulomb explosion model. This model is partially successful in explaining the ionization and subsequent fragmentation of the heavy molecule, I2, exposed to short (sub-100 fs) laser pulses, but even here the fine details are not understood. The dynamics of the fragmentation of the lighter molecules such as N2and CO are not understood at all; one complication is that the time scales of dissociation and stepwise ionization overlap. In the case of the simplest molecular ion, H+2, there has been some progress, leading to the tentative conclusion that bond softening and laser-induced bound states will be important ingredients of a successful theory of multielectron dissociative ionization.