Two different approaches to the problem of how to synthesize macroscopic and nearly defect-free single crystals of polymers are reviewed with the aim of clarifying the underlying physico-chemical principles and of defining the scope of such methods for the further development of the solid-state physics of polymers. The two methods are (i) the topochemical polymerization of diacetylenes and (ii) the simultaneous polymerization and crystallization of trioxane close to the ceiling-equilibrium. Polymers with a backbone of conjugated multiple carbon bonds are formed in the first case via a reaction which proceeds without nucleation phenomena such that the single-crystal nature of a polymerizing crystal is always retained up to quantitative conversion. Single crystals of poly(oxymethylene) grow in the second case following a BCF-type of crystal growth, the growth features being controlled by the nature and the concentration of the catalyst employed.