Nuclear processes such as DNA replication, transcription, and RNA processing each depend on the concerted action of many different protein and RNA molecules. How biomolecules with shared functions find their way to specific locations has been assumed to occur largely by diffusion-mediated collisions. Recent studies have shown that many nuclear processes occur within condensates that compartmentalize and concentrate the protein and RNA molecules required for each process, typically at specific genomic loci. These condensates have common features and emergent properties that provide the cell with regulatory capabilities beyond canonical molecular regulatory mechanisms. We describe here the shared features of nuclear condensates, the components that produce locus-specific condensates, elements of specificity, and the emerging understanding of mechanisms regulating these compartments.