The mitotic spindle faithfully separates the genetic material, and has been reverently observed for well over a century. Across eukaryotes, while the mechanisms for moving chromosomes seem quite conserved, mechanisms for assembling the spindle often seem distinct. Two major pathways for spindle assembly are known, one based on centrosomes and the other based on chromatin, and these pathways are usually considered to be fundamentally different. We review observations of spindle assembly in animals, fungi, and plants, and argue that microtubule assembly at a particular location, centrosomes, or chromatin, reflects contingent, cell-type specific factors, rather than reflecting a fundamental distinction in the process of spindle building. We hypothesize that the essential process for spindle assembly is the motor-driven organization of microtubules that accumulate in the form of dense bundles at or near the chromosomes.