The last few years have seen significant advances in our understanding of the molecular mechanisms of stem-cell-fate specification. New and emerging high-throughput techniques, as well as increasingly accurate loss-of-function perturbation techniques, are allowing us to dissect the interplay among genetic, epigenetic, proteomic, and signaling mechanisms in stem-cell-fate determination with ever-increasing fidelity (Boyer et al. 2005, 2006; Ivanova et al. 2006; Loh et al. 2006; Cole et al. 2008; Jiang et al. 2008; Johnson et al. 2008; Kim et al. 2008; Liu et al. 2008; Marson et al. 2008; Mathur et al. 2008). Taken together, recent reports using these new techniques demonstrate that stem-cell-fate specification is an extremely complex process, regulated by multiple mutually interacting molecular mechanisms involving multiple regulatory feedback loops. Given this complexity and the sensitive dependence of stem cell differentiation on signaling cues from the extracellular environment, how are we best to develop a coherent quantitative understanding of stem cell fate at the systems level? One approach that we and other researchers have begun to investigate is the application of techniques derived in the computational disciplines (mathematics, physics, computer science, etc.) to problems in stem cell biology. Here, we briefly sketch a few pertinent results from the literature in this area and discuss future potential applications of computational techniques to stem cell systems biology.