Cell division is enacted by a microtubule-based, self-assembling macromolecular machine known as the mitotic spindle. In 1986, Kirschner and Mitchison proposed that by undergoing dynamic cycles of growth and disassembly, microtubules search for chromosomes. Capture of microtubules by the kinetochores progressively connects chromosomes to the bipolar spindle. 30 years later, "search and capture" remains the cornerstone of spindle assembly. However, a variety of facilitating mechanisms such as regulation of microtubule dynamics by diffusible gradients, spatially selective motor activities, and adaptive changes in chromosome architecture have been discovered. We discuss how these mechanisms ensure that the spindle assembles rapidly and with a minimal number of errors.