To maintain their genetic integrity, eukaryotic cells must segregate their chromosomes accurately to opposite poles during mitosis. For high-fidelity chromosome segregation, kinetochores must be captured properly on the mitotic spindle before anaphase onset.Correct kinetochore capture by spindle microtubules is achieved in a stepwise manner. Kinetochores are initially captured by the lateral surface of a single microtubule that extends from either spindle pole. Once captured, kinetochores are transported poleward along the microtubule.To assure correct kinetochore capture and transport, microtubules must efficiently locate unattached kinetochores and, after capture, the kinetochores must stabilize associated microtubules.Subsequently, microtubules that extend from the other spindle pole also interact with kinetochores and, eventually, each sister kinetochore attaches to microtubules that extend from opposite poles (this is known as sister kinetochore bi-orientation or amphitelic attachment). To achieve this, mal-oriented kinetochore–spindle-pole connections must be removed, and bi-orientation must be selectively promoted.We discuss how kinetochores are initially captured by microtubules and how sister kinetochores subsequently bi-orient on the mitotic spindle. Although we focus mainly on recent research progress in the budding yeast Saccharomyces cerevisiae, we will also discuss findings in other organisms in this context.