Many recent advances have emerged in the telomere and telomerase fields. This Timeline article highlights the key advances that have expanded our views on the mechanistic underpinnings of telomeres and telomerase and their roles in ageing and disease. Three decades ago, the classic view was that telomeres protected the natural ends of linear chromosomes and that telomerase was a specific telomere-terminal transferase necessary for the replication of chromosome ends in single-celled organisms. While this concept is still correct, many diverse fields associated with telomeres and telomerase have substantially matured. These areas include the discovery of most of the key molecular components of telomerase, implications for limits to cellular replication, identification and characterization of human genetic disorders that result in premature telomere shortening, the concept that inhibiting telomerase might be a successful therapeutic strategy and roles for telomeres in regulating gene expression. We discuss progress in these areas and conclude with challenges and unanswered questions in the field.