Genomes are more than linear sequences. In vivo they exist as elaborate physical structures, and their functional properties are strongly determined by their cellular organization. I discuss here the functional relevance of spatial and temporal genome organization at three hierarchical levels: the organization of nuclear processes, the higher-order organization of the chromatin fiber, and the spatial arrangement of genomes within the cell nucleus. Recent insights into the cell biology of genomes have overturned long-held dogmas and have led to new models for many essential cellular processes, including gene expression and genome stability.