During rapid cooling at about 1000 degrees C/min linear polyethylene crystallizes into spherulitically organized, semicrystalline lamellar stacks. The crystals contain chain conformational defects that are expelled upon reheating. Concomitantly, the crystal grain size increases and surface melting is observed. Close to the melting offset some crystals melt and recrystallize. The crystalline density does not differ from the density of perfect orthorhombic material at any temperature. Small-angle X-ray scattering (SAXS) reveals that the amorphous fraction only completely devitrifies above similar to 17 degrees C. A quench-cooled homogeneous copolymer of ethylene with 5.2 mol % 1-octene devitrifies at -50 degrees C during heating and displays highly branched crystals with a considerable amount of homogeneously distributed defects. Upon heating, these defects migrate toward the crystal surface while crystal fragments and branches preferentially melt, thus leading to an increase of the average crystal lateral dimensions. At rather high temperatures even the most stable crystals melt and recrystallize. The new methodology adopted to extract the crystal lateral dimensions from the SAXS patterns was also applied to the correlation functions calculated from binarized (high-temperature) AFM images. The results are comparable.