  We present a review of the recent progress of theoretical models on the
description of the formation of superheavy nuclei in collisions of heavy
systems. Two sorts of reactions that are the fusion-evaporation mechanism and
the massive damped collisions to produce superheavy nuclei are discussed.
Problems and further improvements of the capture of colliding partners, the
formation of compound nucleus and the de-excitation process are pointed out.
Possible combinations in the synthesis of the gap of the cold fusion and
$^{48}$Ca induced reactions are proposed by the calculations based on the
dinuclear system model and also compared with other approaches. The synthesis
of neutron-rich heavy isotopes near sub-shell closure N=162 via transfer
reactions in the damped collisions of two actinides and the influence of shell
closure on the production of heavy isotopes are investigated. Prospective
possibility to reach superheavy nuclei near N=184 via neutron-rich radioactive
beams of high intensity in the future is discussed.
