Information and catalytic polymers play an essential role in contemporary cellular life, and their emergence must have been crucial during the complex processes that led to the assembly of the first living systems. Polymerization reactions producing these molecules would have had to occur in aqueous medium, which is known to disfavor such reactions. Thus, it was proposed early on that these polymerizations had to be supported by particular environments, such as mineral surfaces and eutectic phases in water-ice, which would have led to the concentration of the monomers out of the bulk aqueous medium and their condensation. This review presents the work conducted to understand how the eutectic phases in water-ice might have promoted RNA polymerization, thereby presumably contributing to the emergence of the ancient information and catalytic system envisioned by the 'RNA-World' hypothesis.