During development, cells undergo a unidirectional course of differentiation that progressively decreases the number of cell types they can potentially become. Stem cells, however, keep their potential to both proliferate and differentiate. A very important issue then is to understand the characteristics that distinguish stem cells from other cell types and allow them to conduct stable proliferation and differentiation. Here, we review relevant dynamical-systems approaches to describe the state transition between stem and differentiated cells, with an emphasis on fluctuating and oscillatory gene expression levels, as these represent the specific properties of stem cells. Relevance between recent experimental results and dynamical-systems descriptions of stem cell differentiation is also discussed.