This Perspective focuses on RNA in biological and nonbiological compartments resulting from liquid-liquid phase separation (LLPS), with an emphasis on origins of life. In extant cells, intracellular liquid condensates, many of which are rich in RNAs and intrinsically disordered proteins, provide spatial regulation of biomolecular interactions that can result in altered gene expression. Given the diversity of biogenic and abiogenic molecules that undergo LLPS, such membraneless compartments may have also played key roles in prebiotic chemistries relevant to the origins of life. The RNA World hypothesis posits that RNA may have served as both a genetic information carrier and a catalyst during the origin of life. Because of its polyanionic backbone, RNA can undergo LLPS by complex coacervation in the presence of polycations. Phase separation could provide a mechanism for concentrating monomers for RNA synthesis and selectively partition longer RNAs with enzymatic functions, thus driving prebiotic evolution. We introduce several types of LLPS that could lead to compartmentalization and discuss potential roles in template-mediated non-enzymatic polymerization of RNA and other related biomolecules, functions of ribozymes and aptamers, and benefits or penalties imparted by liquid demixing. We conclude that tiny liquid droplets may have concentrated precious biomolecules and acted as bioreactors in the RNA World.