The formation of the astral mitotic spindle is initiated at the time of nuclear envelope breakdown from an interaction between the replicated spindle poles (i.e. centrosomes) and the chromosomes. As a result of this interaction bundles of microtubules are generated which firmly attach the kinetochores on each chromosome to opposite spindle poles. Since these kinetochore fibers are also involved in moving the chromosomes, the mechanism by which they are formed is of paramount importance to understanding the etiology of force production within the spindle. As a prelude to outlining such a mechanism, the dynamics of spindle formation and chromosome behavior are examined in the living cell. Next, the properties of centrosomes and kinetochores are reviewed with particular emphasis on the structural and functional changes that occur within these organelles as the cell transits from interphase to mitosis. Finally, a number of recent observations relevant to the mechanism by which these organelles interact are detailed and discussed. From these diverse data it can be concluded that kinetochore fiber microtubules are derived from dynamically unstable astral microtubules that grow into, or grow by and then interact laterally with, the kinetochore. Moreover, the data clearly demonstrate that the interaction of a single astral microtubule with one of the kinetochores on an unattached chromosome is sufficient to attach the chromosome to the spindle, orient it towards a pole, and initiate poleward motion. As the chromosomes move into the region of the forming spindle more astral microtubules become incorporated into the nascent kinetochore fibers and chromosome velocity decreases dramatically. During this time the distribution of spindle microtubules changes from two overlapping radial arrays to the fusiform array characteristic of metaphase cells.