Cells compartmentalize biochemical reactions using organelles. Organelles can be either membrane-bound compartments or supramolecular assemblies of protein and ribonucleic acid known as ‘biomolecular condensates'. Biomolecular condensates, such as nucleoli and germ granules, have been described as liquid like, as they have the ability to fuse, flow, and undergo fission. Recent experiments have revealed that some liquid-like condensates can mature over time to form stable gels. In other cases, biomolecular condensates solidify into amyloid-like fibers. Here we discuss the assembly, organization, and physiological roles of these more stable condensates in cells, focusing on Balbiani bodies, centrosomes, nuclear pores, and amyloid bodies. We discuss how the material properties of these condensates can be explained by the principles of liquid–liquid phase separation and maturation.