Various models for description of the modulation instability of intensive Langmuir oscillations in plasma in one–dimensional representation are discussed. It is noted that the kinetic damping on the electrons can violate the conditions of the modulation instability development due to the suppression of the field at the stage of cavities formation, which in this case can reshape. The hydrodynamic model not quite correctly describes the behavior of particles trapped by the spatially inhomogeneous field, neglecting in fact by their inertia that leads to formation of not only very small–scale and deep plasma density cavities, but also triggers to the peaking regime. Considering ions as particles within framework of so–called hybrid models (when electrons are described as fluid and ions as super–particles) allows to see the appearance of groups of fast ions and premature collapse of density cavities due to the intersection of ion trajectories. These models make possible determination of the energy transmitted to ions and low–frequency collective degrees of freedom. Different models are compared with special emphasis on the comparative dynamics of ion heating with development of the instability of intensive Langmuir oscillations in hot (Zakharov’s model) and cold (Silin’s model) plasma.