Faithful chromosome segregation during anaphase requires that stable microtubule connections are established between chromosomes and both spindle poles by metaphase. Bipolar orientation follows an active period of transient connections between the kinetochores and poles, and tension mediated through attachments between the chromosomes stabilizes those bivalents that have connections to opposite poles. This review focuses on how the chromatids are tied together in the bivalent to ensure proper segregation in the two meiotic divisions. Homologs are partitioned in meiosis I, and reciprocal crossovers, cytologically defined as chiasmata, usually hold the homologs together for this division. The crossovers themselves must be prevented from migrating off the chromatid arms. Binding substances localized to the crossover and sister-chromatid cohesion distal to the crossover have been proposed to prevent loss of chiasmata. Spontaneous nondisjunction events and mutations that disrupt the maintenance of chiasmata are analyzed in the context of these models. Homologs that segregate in meiosis I without chiasmata are briefly discussed. The bivalent must also be constructed so that four chromatids present only two functional kinetochores prior to anaphase I. Cytology and genetic data suggest that the sister kinetochores are duplicated but constrained to act as a single kinetochore. Additionally, centromeric regions of sister chromatids preserve their cohesion until anaphase II, even as cohesion on the sister-chromatid arms is lost at anaphase I. Mutations that specifically disrupt this process are presented.