Almost every cell in the human body is born with a single centrosome. These organelles play an important part in many aspects of cell organisation, and their dysfunction has been linked to a plethora of human pathologies, ranging from cancer to diabetes to microcephaly and dwarfism. Centrosomes are composed of many hundreds of proteins, yet some cells can precisely assemble new centrosomes in just a few minutes, nearly always forming the right number of centrosomes in the right place, at the right time, and growing each centrosome to the right size. Our overarching goal is to understand the molecular mechanisms that allow cells to build such complicated protein machines with such remarkable spatial and temporal precision. We will approach this in two ways: (1) We will generate datasets to construct a near-complete mathematical model of centrosome assembly; (2) We will reconstitute centrosome assembly on the surface of synthetic structures. Together, these approaches will provide both an unparalleled understanding of the principles that govern the biogenesis of a complex organelle, and a conceptual framework with which to probe organelle biogenesis more generally. In the future, these principles may help guide the production of similarly complex human-designed biological nanomachines.