Quantitative approaches are essential for the advancement of strategies to manipulate stem cells or their derivatives for therapeutic applications. Predictive models of stem cell systems would provide the means to pose and validate non-intuitive hypotheses and could thus serve as an important tool for discerning underlying regulatory mechanisms governing stem cell fate decisions. In this paper we review the development of computational models that attempt to describe mammalian adult and embryonic stem (ES) cell responses. Early stochastic models that relied exclusively on statistical distributions to describe the in vitro or in vivo output of stem cells are being revised to incorporate the contributions of exogenous and endogenous parameters on specific stem cell fate processes. Recent models utilize cell specific data (for example, cell-surface receptor distributions, transcription factor half-lives, cell-cycle status, etc.) to provide mechanistic descriptions that are consistent with biologically observed phenomena. Ultimately, the goal of these computational models is to, a priori, predict stem cell output given an initial set of conditions. Our efforts to develop a predictive model of ES cell fate are discussed. The quantitative studies presented in this review represent an important step in developing bioengineering approaches to characterize and predict stem cell behavior. Ongoing efforts to incorporate genetic and signaling network data into computational models should accelerate our understanding of fundamental principles governing stem cell fate decisions.