The formation of membraneless organelles (MLOs) by phase separation has emerged as a new way of organizing the cytoplasm and nucleoplasm of cells. Examples of MLOs forming via phase separation are nucleoli in the nucleus and stress granules in the cytoplasm. The main components of these MLOs are macromolecules such as RNAs and proteins. In order to assemble by phase separation, these proteins and RNAs have to undergo many cooperative interactions. These cooperative interactions are supported by specific molecular features within phase-separating proteins, such as multivalency and the presence of disordered domains that promote weak and transient interactions. However, these features also predispose phase-separating proteins to aberrant behavior. Indeed, evidence is emerging for a strong link between phase-separating proteins, MLOs, and age-related diseases. In this review, we discuss recent progress in understanding the formation, properties, and functions of MLOs. We pay special attention to the emerging link between MLOs and age-related diseases, and we explain how changes in the composition and physical properties of MLOs promote their conversion into an aberrant state. Furthermore, we discuss the key role of the protein quality control machinery in regulating the properties and functions of MLOs and thus in preventing age-related diseases.