Mammalian genomes contain several billion base pairs of DNA that are packaged in chromatin fibres. At selected gene loci, cohesin complexes have been proposed to arrange these fibres into higher-order structures(1-7), but how important this function is for determining overall chromosome architecture and how the process is regulated are not well understood. Using conditional mutagenesis in the mouse, here we show that depletion of the cohesin-associated protein Wapl(8,9) stably locks cohesin on DNA, leads to clustering of cohesin in axial structures, and causes chromatin condensation in interphase chromosomes. These findings reveal that the stability of cohesin-DNA interactions is an important determinant of chromatin structure, and indicate that cohesin has an architectural role in interphase chromosome territories. Furthermore, we show that regulation of cohesin-DNA interactions by Wapl is important for embryonic development, expression of genes such as c-myc (also known as Myc), and cell cycle progression. In mitosis, Wapl-mediated release of cohesin from DNA is essential for proper chromosome segregation and protects cohesin from cleavage by the protease separase, thus enabling mitotic exit in the presence of functional cohesin complexes.