Cell division is a complex process that starts with the formation of a mitotic spindle which segregates chromosomes into two daughter cells at the end of mitosis. The mitotic spindle is a microtubule based micro-machine that carefully orchestrates the forces generated by motor proteins and its functionality relies on the accuracy of spindle self-organization. Errors in spindle self-organization can lead to missegregation which produces aneuploidy, a state with irregular number of chromosomes. Aneuploidy in combination with propensity of gaining and losing chromosome with high frequency can create a domino effect which leads to the development of tumor tissues. In this thesis we aim to understand the key processes behind the formation of an antiparallel bundle of a mitotic spindle as well as explore what are the consequences of errors during cell division after multiple generations. To understand tumor evolution from healthy cells we develop a “macro-karyotype model” and show that the perturbed number of chromosomes in tumor cells arises predominantly from a faster division of cells characterized by a specific combination of chromosomes, or together with irregular cell death. This theoretical result explains experimentally observed combination of chromosomes in different stages of tumor development including a small number of aneuploid cells in pretumor stages as well as highly aneuploid cells in tumor stage. We also investigate the selforganization of microtubules into an antiparallel bundle and for that purpose develop a mathematical model that includes the dynamics of microtubules and motor proteins. By solving the model, we show that microtubules from each pole search for those from the opposite pole by performing a random angular movement. Upon contact, two microtubules slide sideways along each other in a directed manner toward the antiparallel configuration. We introduce the contour length of microtubules as a measure of the activity of motors that drives microtubule sliding, which reveals that minus-end-directed motility drives microtubules into an antiparallel organization. In conclusion, our theoretical approach contributes to a better understanding of the complex process of cell division and the long-term consequences of its malfunctioning and thereby connects two different timescales relevant for proper cell functioning.