The recent progress in the understanding of the melting kinetics of polymer crystals was reviewed. The melting behavior of folded-chain crystals (FCC) of polymers becomes seriously complicated due to the metastability of FCC causing melting-recrystallization cycles and reorganization of crystals. Conventional calorimetry of the melting under constant rate of heating suggested a heating rate dependence of melting peak temperature, which is understood as a superheated melting kinetics. A morphological observation of melting of single crystals supported this behavior. Recent progress of chip-sensor fast scanning calorimetry (FSC) also confirmed the behavior and enabled the examination of isothermal melting kinetics. The results suggested an exponential dependence of melting rate on superheating, which can be interpreted as a consequence of inhomogeneous stability of crystalline stems derived from broad variations of chain-folding conformations. As a further application of FSC to organic crystals, melting kinetics of sucrose is also reviewed.