Modern microscopy techniques allow us to observe specifically tagged proteins in live cells. We can now see directly that many cellular structures, for example mitotic spindles, are in fact dynamic assemblies. Their apparent stability results from out-of-equilibrium stochastic interactions at the molecular level. Recent studies have shown that the spindles can form even after centrosomes are destroyed, and that they can even form around DNA-coated beads devoid of kinetochores. Moreover, conditions have been produced in which microtubule asters interact even in the absence of chromatin. Together, these observations suggest that the spindle can be experimentally deconstructed, and that its defining characteristics can be studied in a simplified context, in the absence of the full division machinery.