Cells are the functional units of life, and their division ensures that life is propagated across generations. In its outline, cell division is elegant and simple. Chromosomes, which harbor the genetic material, are first replicated in the mother cell. Then, in the following phase, named mitosis (or meiosis, a specialized cell division occurring in the germ line), chromosomes are distributed to the two daughter cells. The orchestrated ballet of chromosomes, with its remarkable precision, is the action of a molecular structure, the mitotic spindle. The simplicity of the task contrasts with the relative complexity of the structure, which is self-assembled from hundreds of different macromolecules. How can we make inroads into the dissection of this mechanism? In our program, called BIOMECANET (which stands for Integration of the Biochemical and Mechanical Networks of Cell Division), we have the ambition to use the building blocks of cell division to reconstitute in vitro the crucial molecular events that underlie this process. At the same time, we will simulate spindle assembly in a computer to make sense of its dynamics and understand how function emerges from structure. For instance, we will reconstitute the mitotic spindle, the kinetochores (the structure that links chromosomes to the mitotic spindle), and the regulatory machinery that coordinates their interactions. We will achieve this goal by combining a minimal – yet very complex – set of components sufficient to mimic the most fundamental dynamics of this process. We will then analyse the behavior of these molecular systems using in silico simulations of unprecedented complexity and realism. Besides investigating a fundamental biological process, our work will also shed light on the circumstances that cause the cell division process to fail, resulting in chromosome imbalances that are associated with many human diseases, most notably cancer.