Telomeres are DNA structures which serve to stabilize chromosomes. In human cells telomeres progressively shorten with each cell division leading to eventual chromosome instability and cell death. Telomerase is a DNA polymerase which is required for the maintenance of telomeres. Therefore, telomeres and telomerase play a role in the regulation of the life span of the cell. Human cells express low levels of telomerase, however when telomere length reaches a critical level abnormal activation of telomerase can lead to immortalization and uncontrolled proliferation. This process has been associated with the development of many leukaemias and lymphomas. Understanding these processes in normal and malignant cells could lead to therapies which target the telomere/telomerase complex.