Linear organization of the genome requires mechanisms to protect and replicate chromosome ends. To this end eukaryotic cells evolved telomeres, specialized nucleoproteic complexes, and telomerase, the enzyme that maintains the telomeric DNA. Telomeres allow cells to distinguish chromosome ends from sites of DNA damage. In mammalian cells this is accomplished by a protein complex, termed shelterin, that binds to telomeric DNA and is able to shield chromosome ends from the DNA damage machinery. In recent years, we have seen major advances in our understanding of how this protein complex works due to the generation of mouse models carrying mutations of individual shelterin components. This review will focus on our current understanding of how the shelterin complex is able to suppress the DNA damage response pathways, and on the cellular and organismal outcomes of telomere dysfunction.