Telomeres are DNA-protein complexes located at the ends of linear chromosomes in most eukaryotic cells. Telomeres are vital components of chromosome integrity and cell proliferation. They protect internally located genes from degradation due to incomplete DNA replication, and they also mask natural DNA ends from being recognized as DNA breaks. While being guardians of genome integrity, telomeres can also be vulnerable to damage and inappropriate repair. Dysfunction in telomere maintenance can lead to serious illnesses in humans, including cancer. Cancers achieve immortalization through telomere elongation either through the activation of specialized enzyme telomerase or Alternative Lengthening of Telomeres (ALT) pathway. This review highlights the structure and the function of telomeres in yeast and humans, discusses telomere binding proteins and their roles in telomere maintenance, and briefly describes the implications of telomere dysfunction on human health.