Kinetochores are DNA-protein structures that attach and move chromosomes along the microtubules of the mitotic spindle. This review focuses on centromeres and kinetochores from the budding yeast Saccharomyces cerevisiae. Because of their relative simplicity, budding yeast centromeres are particularly well suited to detailed molecular analysis. The review begins with a description of chromosome movement and microtubule attachment in living yeast cells. We then describe how centromeric DNA was cloned and analyzed and how this analysis has led to the isolation of centromere-binding proteins by both biochemical and genetic means. Modes of microtubule attachment in vitro are discussed with an attempt to relate in vitro studies to the events that occur in vivo. Finally, we conclude with a speculative model for the organization of the budding yeast centromere a consideration of possible future developments.