The abiotic formation of biopolymers from their monomeric building blocks and the emergence of cellular structures are still unsolved problems in the origin of life investigation. In this frame soft matter concepts of self-assembly, collective ordering and phase transitions can give an outstanding contribution, complementary to the bio-chemical approaches. I will talk about my recent works on the spontaneous ordering of RNA and DNA fragments into soft phases typical of liquid crystals, showing relevant features for promoting the polymerization and selection of nucleic acids. I will also talk about ongoing development of my investigation aimed at expanding this approach to complex biomolecular mixtures, where co-assembly of nucleic acids and peptides or amphiphilic molecules drives the formation of complex coacervates with different degrees of order.