The molecular characteristics which determine the melting points of high polymer crystals are considered, and it is shown that the properties of monomeric crystals often throw light on those of the polymers. The principal factors controlling melting points appear to be molar cohesion energy (of the whole molecule for monomers, or per chain unit for polymers), molecular flexibility (due to rotation round bonds), and molecular shape effects. Figures for the cohesion energy increments of a number of chain units and substituent groups are given, and melting points of polymer series are correlated with cohesion energy per chain unit. The flexibility factor is less easy to assess; barriers to rotation in appropriate monomer molecules are relevant, but available data are very rough. The approach therefore is mainly by empirical and comparative methods. When plotted against cohesion energy per chain unit, the melting points of various series of aromatic polyesters and polyurethans fall within the same band, while those of the polyamides lie on the whole higher and those of the aliphatic polyesters, polyethers, polythioethers and polydisulfides much lower. The differences are attributed to difference of molecular flexibility arising from the presence of easily rotating O-C, S-C and S-S bonds. The low melting points of rubber and other unsaturated polymers are attributed to the fact (which can now be regarded as definitely established by independent evidence) that rotation round single bonds which are adjacent to double C=C bonds is easier than in saturated chains. Easily rotating bonds which are inclined to each other, as in cis isomers, confer greater chain flexibility than the parallel bonds in trans isomers, and thus lead to lower melting points. The marked odd-even effects in saturated molecules which run through the whole of organic chemistry (the even members always melting higher than the odd) are attributed to similar effects arising from the fact that the end bonds of an odd CH2 sequence are inclined to each other while those at the ends of an even sequence are parallel.