In any stem cell, the accrual of mutations can have deleterious effects. In the earliest stages of the development of a multicellular organism, pathogenic mutations in a pluripotent stem cell can be propagated to affect many cells and tissues. Therefore, the avoidance of mutations in pluripotent cells is of the utmost importance. Many stem cells achieve low mutation rates in contrast to their terminally differentiated counterparts, with pluripotent embryonic stem cells (ESCs) displaying among the lowest. The study of the bases of this property is incomplete, though several explanations exist. ESCs employ high-fidelity DNA repair mechanisms, exhibit unique cell cycle checkpoint controls, and rapidly commit to cell death when exposed to genotoxins. Crucially, the responses of ESCs to DNA replication stress are poorly understood, representing a gap in the foundation of our understanding of stem cell mutation avoidance. This is of consequence to the expanding practice of using induced pluripotent stem cells (iPSCs) to regenerate dysfunctional or damaged tissues. With this knowledge in hand, I aimed to characterize the responses of pluripotent stem cells to several types of replication stress. As replication stress responses center around protein kinases that drive cell cycle checkpoint signaling, the manipulation of these kinases was crucial to the study. Many kinases involved in DNA replication stress are essential genes, making this manipulation challenging. With the ability to leverage small molecule drugs to inhibit cellular processes, such manipulation could be readily achieved. Therefore, I induced replication stress with genotoxic compounds and combined this with small molecule inhibitors to dissect the response to different stresses. By combining this approach with fundamental methods such as DNA content analysis via flow cytometry and western blots, I was able to determine which cell cycle checkpoints are activated in response to certain stresses. This work identifies several potential mutation avoidance mechanisms in pluripotent stem cells that may extend to many other stem cell types.