The spindle is a self-assembled, bipolar structure responsible for segregating chromosomes to daughter cells during cell division. During spindle formation, molecular motors and other proteins organize microtubules (MTs), dynamic rod-like polymers, into a fusiform array. How these assembly factors organize MTs into spindles of the appropriate morphology is not fully understood. The process of organelle self-assembly is particularly apparent in meiotic spindles, which assemble in the absence of centrosomes and must align MTs initially nucleated at random orientations. Additionally, meiotic spindles can be orders of magnitude smaller than the cell in which they assemble. Because of this size disparity, the cell boundary cannot act as a cue for spindle length, leaving cytoplasmic factors to determine proper spindle size.Previously, cytoplasmic extracts from Xenopus laevis eggs have been used as a complex, cell-free experimental system in which to study meiotic spindle assembly. Beginning with a simplified model of the X. laevis meiotic spindle, I used computer simulations to examine the contributions of various spindle components to spindle maintenance and morphology. In parallel, I used egg extracts from two closely related species of Xenopus, X. laevis and X. tropicalis, to discover new mechanisms and to test predicted mechanisms of spindle formation and length control. This dissertation contains my work integrating these computational and experimental approaches to elucidate mechanisms of meiotic spindle assembly, maintenance, and length regulation.Many components contributing to spindle assembly have been identified, but how these components organize MTs into the bipolar architecture of the spindle has not been demonstrated. To explore mechanisms of MT organization along the pole-to-pole axis, I simulated meiotic spindle assembly in two dimensions (2D) using dynamic MTs, a MT crosslinking force, and a tetrameric molecular motor. The structures that formed consisted of aligned, antiparallel MTs, but spindle pole formation required the addition of minus end-directed transport of MT depolymerization activity. Simulations generated MT structures that qualitatively and quantitatively reproduced features and phenotypes of meiotic spindles assembled in Xenopus egg extracts. By varying different parameters, I demonstrated the importance of localized MT destabilization and spatially dispersed nucleation to spindle organization.Simulated spindles exemplified how a global balance between assembly and disassembly can regulate the size of a steady state structure. Using the computational model, I examined how steady state spindle length is dynamically regulated by specific assembly mechanisms and how these mechanisms generate the robustness expected of structures in stable equilibrium. The model illustrated how factors affecting the dispersion of MT minus ends, including MT catastrophe, transport, depolymerization, and severing, determined spindle length. The introduction of kinetochore-MTs (k-MTs) as an additional source of assembly lengthened spindles, in some cases causing non-steady state expansion of MT structures, but such effects could be offset by complementary increases in disassembly mechanisms.The spindle assembly mechanisms present in the simplified computational model were able to organize MTs and regulate spindle length, but the significance of these mechanisms to the complex meiotic spindles formed in Xenopus egg extracts remained to be tested. Egg extracts from X. laevis and X. tropicalis represented an ideal system for such experiments, because spindles formed in the two extracts were of significantly different lengths, suggesting the utilization of different assembly mechanisms. Additionally, the extracts were compatible - spindles formed in mixed X. laevis-X. tropicalis extracts - and spindle length scaled with the mixing ratio, allowing us to manipulate the relative strength of assembly mechanisms to determine their effect on spindle morphology.The factors regulating spindle size in these egg extracts have not been identified but are known to be cytoplasmic. Guided by previous results and computational predictions, I characterized the contribution of MT destabilization activity to spindle formation and size. I demonstrated that MT destabilization is elevated in X. tropicalis due to intrinsic differences in the MT severing protein katanin. Katanin inhibition lengthened spindles in both species. However, in X. tropicalis spindles, coordination between spindle MTs and kinetochore fibers (k-fibers) was lost as k-fibers extended through and disrupted spindle poles, reminiscent of the continual expansion of k-MTs observed in simulations. By varying chromosome number in the spindle, I confirmed the computational prediction that beyond a threshold number of stable k-fibers, k-fiber growth overwhelms MT destabilization and prevents spindles from reaching a steady state. Finally, I investigated the cause of the relatively mild phenotype in X. laevis spindles upon reduction of katanin-mediated severing and found that this insensitivity was not due to elevated compensatory kin-13 activity.In summary, complementary computational and experimental approaches were utilized to elucidate mechanisms of MT organization and length regulation in the meiotic spindle, specifically identifying MT severing as a regulator of Xenopus spindle morphology.