Sister-chromatid cohesion, thought to be primarily mediated by the cohesin complex, is essential for chromosome segregation. The forces holding the two sisters resist the tendency of microtubules to prematurely pull sister DNAs apart and thereby prevent random segregation of the genome during mitosis, and consequent aneuploidy. By counteracting the spindle pulling forces, cohesion between the two sisters generates the tension necessary to stabilize microtubule-kinetochore attachments. Upon entry into anaphase, however, the linkages that hold the two sister DNAs must be rapidly destroyed to allow physical separation of chromatids. Anaphase cells must therefore possess mechanisms that ensure faithful segregation of single chromatids that are now attached stably to the spindle in a manner no longer dependent on tension. In the present review, we discuss the nature of the cohesive forces that hold sister chromatids together, the mechanisms that trigger their physical separation, and the anaphase-specific changes that ensure proper segregation of single chromatids during the later stages of mitosis.