Telomeres are distinctive structures, composed of a repetitive DNA sequence and associated proteins, which enable cells to distinguish chromosome ends from DNA double-strand breaks. Telomere alterations, caused by replication-mediated shortening, direct damage or defective telomere-associated proteins, usually generate chromosomal instability, which is observed in senescence and during the immortalization process. In cancer cells, this chromosome instability could be extended by their ability to 'repair' chromosomes and terminate in break-fusion-bridge cycles. Dysfunctional telomeres can be healed by activation of telomerase or by the 'alternative mechanism' of telomere lengthening. Activation of such telomere maintenance mechanisms may help to preserve the integrity of chromosomes even if they play a role in chromosomal instability. This review focuses on molecular processes involved in telomere maintenance and chromosomal instability associated with dysfunctional telomeres in mammalian cells.