Eukaryotic cells are complex structures capable of coordinating numerous biochemical reactions in space and time. Key to such coordination is the subdivision of intracellular space into functional compartments. Compartmentalization can be achieved by intracellular membranes, which surround organelles and act as physical barriers. In addition, cells have developed sophisticated mechanisms to partition their inner substance in a tightly regulated manner. Recent studies provide compelling evidence that membraneless compartmentalization can be achieved by liquid demixing, a process culminating in liquid-liquid phase separation and the formation of phase boundaries. We discuss how this emerging concept may help in understanding dynamic reorganization of subcellular space and highlight its potential as a framework to explain pathological protein assembly in cancer and neurodegeneration.