Telomeres are tandem repeats of DNA that are present at the end of a linear chromosome. They play a critical role in providing chromosome-end protection. There are certain binding sites of proteins, called shelterins, in the telomere structure that play a critical role in telomere protection. Telomeres are elongated by telomerase enzymes. In normal human somatic cells, telomerase is inactivated, and consequently, telomeres shorten with each cell cycle. Short telomeres can play opposing roles in carcinogenesis. First, short telomeres can play an essential role in stopping the occurrence of cancer. Second, short telomeres can lead to genome instability, which may result in the formation of some cancer cells. However, cancer cell telomeres can be lengthened by the reactivation of telomerase or alternative lengthening of telomeres (ALT) mechanisms. ALT is a homologous recombination-based mechanism that depends on the RAD52 gene. This review summarises the role of short and long telomeres in the initiation and growth of cancer cells.