The nucleus is perhaps the most familiar organelle within eukaryotic cells, serving as a compartment to house the genetic material. The nuclear volume is subdivided into a variety of functional and dynamic nuclear bodies not separated from the nucleoplasm by membranes. It has been hypothesized that aqueous phase separation brought about by macromolecular crowding may be in part responsible for these intranuclear compartments. This chapter discusses macromolecular solution chemistry with regard to several common types of phase separation in polymer solutions as well as to recent evidence that suggests that cytoplasmic and nuclear bodies may exist as liquid phases. We then examine the functional significance of phase separation and how it may serve as a means of compartmentalizing various nuclear activities, and describe recent studies that have used simple model systems to generate coexisting aqueous phase compartments, concentrate molecules within them, and perform localized biochemical reactions.