Human pluripotent stem cells, including embryonic and induced pluripotent stem cells, hold enormous potential for the treatment of many diseases, owing to their ability to generate cell types useful for therapeutic applications. Currently, many stem cell culture propagation and differentiation systems incorporate animal-derived components for promoting self-renewal and differentiation. However, use of these components is labor intensive, carries the risk of xenogeneic contamination and yields compromised experimental results that are difficult to duplicate. From a biomaterials perspective, the generation of an animal- and cell-free biomimetic microenvironment that provides the appropriate physical and chemical cues for stem cell self-renewal or differentiation into specialized cell types would be ideal. This review presents the use of natural and synthetic polymers that support propagation and differentiation of stem cells, in an attempt to obtain a clear understanding of the factors responsible for the determination of stem cell fate.