Liquid-liquid phase separation (LLPS) underlies the formation of intracellular membraneless compartments in biology and may have played a role in the formation of protocells that concentrate key chemicals during the origins of life. While LLPS of simple systems, such as oil and water, is well understood, many aspects of LLPS in complex, out-of-equilibrium molecular systems remain elusive. Here, the author discusses open questions and recent insights related to the formation, function and fate of such condensates both in cell biology and protocell research.