A scientific review presents biomaterials for the feeder-free culture of human embryonic stem cells (hESC) and induced pluripotent stem cells (iPSC). Tissue-specific stem cell niches provide crucial cell-cell contacts and paracrine signaling. The extracellular matrix ECM) keeps stem cells in the niche and serves to initiate signal transduction, while locally concentrated glycosaminoglycans (GAGs) provide soluble growth factors or cytokines. It will be highly beneficial to design, construct, and reproduce the microenvironment and niche of pluripotent stem cells in vitro with biomacromolecules and synthetic polymers. Culture materials derived from biomacromolecules and synthetic polymers have been used to support the propagation of hESCs and human iPSCs while maintaining their pluripotency.