This review covers the application of polymeric materials in stem cell bioengineering. Main emphasis is directed towards current material design concepts that mimic distinct exogenous signals of the stem cell microenvironment. Progress within the field of stem cell-specific biomaterials will be discussed, focusing on pluripotent, hematopoietic, mesenchymal and neural stem cells. The future role of biomaterials will be outlined with possible applications for cell reprogramming and engineering cancer cell microenvironments.