Telomeres are repetitive sequences at the natural ends of linear eukaryotic chromosomes that protect these from recognition as chromosome breaks. Their ability to do so critically depends on the binding of sufficient quantities of functional shelterin, a six-unit protein complex with specific and crucial roles in telomere maintenance and function. Insufficient telomere length, leading to insufficient concentration of shelterin at chromosome ends, or otherwise crippled shelterin function, causes telomere deprotection. While contributing to aging-related pathologies, loss of telomere protection can act as a barrier to tumorigenesis, as dysfunctional telomeres activate DNA-damage-like checkpoint responses that halt cell proliferation or trigger cell death. In addition, dysfunctional telomeres affect cancer development and progression by being a source of genomic instability. Reviewed here are the different approaches that are being undertaken to investigate the mammalian cellular response to telomere dysfunction and its consequences for cancer. Furthermore, it is discussed how current and future knowledge about the mechanisms underlying telomere damage responses might be applied for diagnostic purposes or therapeutic intervention.