There is a growing body of evidence to suggest that stem cell populations from both the embryo and the adult are heterogeneous in their gene expression patterns. However, the underlying mechanisms are not well understood. This thesis explores cell-to-cell variability in both multipotent and pluripotent stem cell populations using mathematical models to provide a theoretical framework to understand the collective dynamics of stem cell populations. In the first part of the thesis we investigate the possibility that fluctuations in the transcription factor Nanog { which is central to the embryonic stem cell transcriptional regulatory network (ESCTRN) { regulate population variability by controlling important feedback mechanisms. Our analyses reveal the ESC TRN is rich in feedback, with global feedback structure critically dependent on Nanog, Oct4 and Sox2, which collectively participate in over two thirds of all feedback loops. Using a general measure of feedback centrality we show that removal of Nanog severely compromises the global feedback structure of the ESC TRN. These analyses indicate that Nanog fluctuations regulate population heterogeneity by transiently activating different regulatory subnetworks, driving transitions between a Nanog-expressing, feedback-rich, robust and self-perpetuating pluripotent state and a Nanog-diminished, feedback-sparse and differentiation-sensitive state. The majority of studies characterising heterogeneity in Nanog expression have used live-cell fluorescent reporter strategies. However, recent evidence suggests that these reporters may not give a faithful reflection of endogenous Nanog expression because the introduction of the reporter construct can perturb the kinetics of the underlying regulatory network. To investigate the role of Nanog further we therefore sought to model in detail the dynamics of Nanog expression in heterozygous fluorescent knock-in reporter cell lines. We develop chemical master equation, chemical Langevin equation and reaction rate equation models of the reporter system to determine how this might disturb normal Nanog transcriptional control. Our analyses indicate that the reporter construct can weaken the strength of autoactivatory feedback loops that are central to Nanog regulation, and thereby qualitatively perturbs endogenous Nanog dynamics. These results question the efficacy of commonly used reporter strategies and therefore have important implications for the design and use of synthetic reporters in general, not just for Nanog. In the second part of this thesis we consider the dynamics of populations of multipotent adult hematopoietic stem cells (HSCs). It is known that fluctuations within individual HSCs allow them to transit stochastically between functionally distinct metastable states, while the overall population distribution of expression remains stable. To investigate the relationship between single cell and population-level dynamics we propose a theoretical framework that views cellular multipotency as an instance of maximum entropy statistical inference, in which an underlying ergodic stochastic process gives rise to robust variability within the cell population. We illustrate this view by analysing expression fluctuations of the stem cell surface marker Sca1 in mouse HSCs and find that the observed dynamics naturally lie close to a critical state, thereby producing a diverse population that is able to respond rapidly to environmental changes. Although we focus on Sca1 dynamics, comparable expression fluctuations are known to generate functional diversity in other mammalian stem cell systems, including in pluripotent stem cells. Thus, the generation of ergodic expression fluctuations may be a generic way in which cell populations maintain robust multilineage differentiation potential under environmental uncertainty.