<p>Centromeres provide the chromosomal scaffold for the assembly of the kinetochore complex, thereby linking replicated sister chromatids to the mitotic spindle, driving their segregation into nascent daughter cells. The location and maintenance of centromeres rely, in large part, on a unique conserved chromatin domain, defined by nucleosomes containing the histone H3 variant, Centromere Protein A (CENP-A), whose discovery 40 years ago we now celebrate. Current models place CENP-A, along with many of its orthologs, at the centre of a self-propagating epigenetic feedback loop that heritably maintains centromere position through mitotic and meiotic divisions. CENP-A is stably recycled through DNA replication but requires replenishment each cell cycle. In many organisms, assembly is restricted to G1 phase, indicating tight cell cycle control of the assembly machinery. Here, we provide a historical overview of the discoveries that led to current models of cell cycle control of centromere assembly, starting with early models of regulation to the intricate, multi-layered phosphoregulation revealed to date. Our review focuses primarily on the human and other animal systems, in which the current view is that negative and positive control through cyclin-dependent kinases and Polo-like kinase 1 combine to link CENP-A assembly to mitotic exit. Cell cycle-coupled CENP-A assembly has been attributed to so-called licensing or priming events. We discuss the validity of these models and terminology and highlight key outstanding questions that remain unanswered.</p>