Nucleic acids (NAs) in modern biology accomplish a variety of tasks, and the emergence of primitive nucleic acids is broadly recognized as a crucial step for the emergence of life. While modern NAs have been optimized by evolution to accomplish various biological functions, such as catalysis or transmission of genetic information, primitive NAs could have emerged and been selected based on more rudimental chemical–physical properties, such as their propensity to self-assemble into supramolecular structures. One such supramolecular structure available to primitive NAs are liquid crystal (LC) phases, which are the outcome of the collective behavior of short DNA or RNA oligomers or monomers that self-assemble into linear aggregates by combinations of pairing and stacking. Formation of NA LCs could have provided many essential advantages for a primitive evolving system, including the selection of potential genetic polymers based on structure, protection by compartmentalization, elongation, and recombination by enhanced abiotic ligation. Here, we review recent studies on NA LC assembly, structure, and functions with potential prebiotic relevance. Finally, we discuss environmental or geological conditions on early Earth that could have promoted (or inhibited) primitive NA LC formation and highlight future investigation axes essential to further understanding of how LCs could have contributed to the emergence of life.