Although mechanisms of telomere protection are well-defined in many types of differentiated cells, it is poorly understood how pluripotent stem cells sense and respond to telomere dysfunction. This thesis reports on the generation of novel human induced pluripotent stem cell (iPSC) models to study DNA damage signaling, cell cycle, and transcriptome-level changes in response to experimentally induced telomere dysfunction during pluripotency. We first engineer human iPSCs with an inducible TRF1-FokI fusion protein to acutely induce double strand breaks at telomeres. Using this model, we demonstrate that TRF1-FokI DSBs activate an ATR-dependent DNA damage response, which leads to p53-independent cell cycle arrest in G2. We show that telomerase is largely dispensable for survival and telomere length maintenance following telomeric breaks, which instead appear to be repaired by a mechanism bearing hallmarks of lengthening by homologous recombination. Next, we generate a human iPSC line with an inducible dominant-negative TRF2 allele to initiate acute telomere uncapping and show that this model does not phenocopy Trf2 deletion in mouse embryonic stem cells. Lastly, we optimize a strategy for directed differentiation of colonic organoids from engineered iPSCs, and we describe our efforts to study responses to telomere dysfunction in this system. Our findings reveal distinct iPSC-specific responses to telomere dysfunction and build upon existing organoid models to enable the study of telomere biology in differentiated tissues.