Telomere is guanine-rich DNA sequence with a protein complex known as shelterin present at the chromosomal ends to protect it from destruction and is known to play a key role in aging. Telomerase is a telomeric DNA elongating enzyme, which comprises the central key components for telomeric DNA synthesis. The main objective of this review was to explore the structure and function of telomere and telomerase, and their intervention in aging, stem cells, and cancer cells. The induction of various telomeropathies and age-related diseases by Telomerase RNA component (TERC) impairment is well explained. Telomeropathies refer to bone marrow failures such as dyskeratosis congenita, aplastic anemia, etc. Telomere and telomerase have become the targets for age-related therapies, stem cell therapies, and cancer therapies. This article throws light on the telomerase-related therapies with natural compounds in regenerative medicine and cancer treatment. Telomerase inhibitors like nucleoside ligands and G4 ligands are explained in the context of anti-cancer drugs. The association of TERT promoter mutations with cancer is discussed. We conclude that understanding telomerase mechanisms in stem cells and cancer cells paves a way to translate stem cells, cancer cells, and age-related research into effective therapies. The dynamic features of telomerase and telomeres make their structural and biochemical studies difficult. Hence, further meticulous studies can be done on single-molecule approaches to facilitate feasible and effective studies of telomerase and telomere component functioning.