Telomeres are the nucleoprotein structures at the end of linear eukaryotic chromosomes required for genome stability. Telomerase is the specialized enzyme deputed to their elongation. Maintenance of a proper telomere structure, an accurate regulation of telomerase biogenesis and activity, as well as a correct telomere-telomerase interaction and a faithful telomeric DNA replication are all processes that a cell has to precisely control to safeguard its functionality. Here, we review key factors that play a role in the development of these processes and their relationship with human health.