A review with 57 refs. covering nucleation modes and models of polymer crystallization kinetics. The classical models assume the rate of crystallization to be related to temperature only. For materials exhibiting low molecular mobility, e.g., polymers, time effects appear justified. Ziabicki's model [51-53] allows the rate to be related to time. In thermal nucleation, this relation stems from the delay of the steady-state condition to become established under specific external conditions. The athermal mechanism of nucleation produces another time effect. It involves no potential barriers to be overcome by a cluster to become a nucleus and proceeds only on account of the change in the criterion for the nucleus stability (critical size) as external conditions are modified. Experiments showed the (iso and non-isothermal) crystallization rate to be directly related to time. The underlying phenomenon involves the athermal nucleation occurring on crystal residues left in the melt and the relaxation effect upon subsequent thermal nucleation. The applicability of Ziabicki's model is demonstrated.