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Stem cells have the capability to self-renew and maintain their undifferentiated state or to differentiate into one or more specialised cell types. Stem cell expansion and manipulation ex vivo is a promising approach for engineering cell replacement therapies, and endogenous stem cells represent potential drugable targets for tissue repair. Before we can harness stem cells' therapeutic potential, we must first understand the intracellular mechanisms controlling their fate choices. These mechanisms involve complex signal transduction and gene regulation networks that feature, for example, intricate feed-forward loops, feedback loops and cross-talk between multiple signalling pathways. Systems biology applies computational and experimental approaches to investigate the emergent behaviour of collections of molecules and strives to explain how these numerous components interact to regulate molecular, cellular and organismal behaviour. Here we review systems biology, and in particular computational, efforts to understand the intracellular mechanisms of stem cell fate choice. We first discuss deterministic and stochastic models that synthesise molecular knowledge into mathematical formalism, enable simulation of important system behaviours and stimulate further experimentation. In addition, statistical analyses such as Bayesian networks and principal components analysis (PCA)/partial least squares (PLS) regression can distill large datasets into more readily managed networks and principal components that provide insights into the critical aspects and components of regulatory networks. Collectively, integrating modelling with experimentation has strong potential for enabling a deeper understanding of stem cell fate choice and thereby aiding the development of therapies to harness stem cells' therapeutic potential.