Telomeres are specialized nucleoprotein structures at the ends of linear chromosomes that prevent the activation of DNA damage response and repair pathways. Numerous factors localize at telomeres to regulate their length, structure and function, to avert replicative senescence or genome instability and cell death. In humans, Mendelian defects in several of these factors can result in abnormally short or dysfunctional telomeres, causing a group of rare heterogeneous premature-ageing diseases, termed telomeropathies, short-telomere syndromes or telomere biology disorders (TBDs). Here, we review the TBD-causing genes identified so far and describe their main functions associated with telomere biology. We present molecular aspects of TBDs, including genetic anticipation, phenocopy, incomplete penetrance and somatic genetic rescue, which underlie the complexity of these diseases. We also discuss the implications of phenotypic and genetic features of TBDs on fundamental aspects related to human telomere biology, ageing and cancer, as well as on diagnostic, therapeutic and clinical approaches.