The nucleoprotein complexes that cap the very ends of the eukaryotic chromosomes, named telomeres, are indispensable for cell viability. Telomeric DNA shortens in each cell division until it cannot exert end-protective functions in human somatic cells. Additionally, several proteins have been described to play a key role in telomere homeostasis preventing chromosome extremities to be recognized as double-stranded breaks (DSBs). When telomeres become dysfunctional, either through excessive shortening or due to defects in the proteins that form its structure, they trigger p53/pRb pathways what limits proliferative lifespan. Impairment of telomere function together with a compromised senescence/apoptosis response leads to chromosome instability. Fusions between dysfunctional telomeres or even between dysfunctional telomeres and DSBs can initiate breakage-fusion-bridge (BFB) cycles. Initially, telomere fusions were proposed to cause only structural abnormalities. Nevertheless, changes in chromosome number have also emerged as a possible consequence of alterations in end capping. Here we review the main aspects of telomeres and telomere-based chromosome instability, highlighting why they have been proposed as a driving force for tumourigenesis.